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BEGIN:VEVENT
SUMMARY:Tsarev S.P (Siberian Federal University\, Krasnoyarsk\, Russia)
DTSTART:20200527T110000Z
DTEND:20200527T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/1/">
 Discrete orthogonal polynomials: anomalies of time series and boundary eff
 ects of polynomial filters</a>\nby Tsarev S.P (Siberian Federal University
 \, Krasnoyarsk\, Russia) as part of Mathematical models and integration me
 thods\n\n\nAbstract\nWe describe a new result in the classical theory of u
 nivariate discrete orthogonal polynomials: extremely fast decay of their v
 alues near the interval boundary for polynomials of sufficiently high degr
 ee. This effect dramatically differs from the behavior of much more popula
 r in mathematical curricula continuous orthogonal polynomials.\n\nThe prac
 tical importance of this new result for the theory of discrete polynomial 
 filters (widely applied for detection of anomalies of time series of measu
 rements) is demonstrated on the practical example of detection of outliers
  and small discontinuities in the publicly available GPS and GLONASS traje
 ctories.\n\nDiscrete polynomial filters\, on one hand\, can detect very sm
 all anomalies in sparse time series (with amplitude of order 10^(-11) rela
 tive to the typical values of the time series). On the other hand our gene
 ral result limits sensitivity of polynomial filters near the boundary of t
 he time series. The main problem in practical applications of the discusse
 d method is numerical instability of construction of the discrete orthogon
 al polynomials of high degree.\n\nZoom link for the talk: https://us04web.
 zoom.us/j/73902155099?pwd=ZnhXVUtIbUhPNmk4MFJ2dGpLNllZUT09\n
LOCATION:https://researchseminars.org/talk/mmandim/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.V. Meleshko\, N.P. Moshkin\, A.G. Petrova\, V.V. Pukhnachev
DTSTART:20200603T110000Z
DTEND:20200603T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/2/">
 On exact analytical solutions of equations of Maxwell incompressible visco
 elastic medium</a>\nby S.V. Meleshko\, N.P. Moshkin\, A.G. Petrova\, V.V. 
 Pukhnachev as part of Mathematical models and integration methods\n\n\nAbs
 tract\nUnstationary and stationary two-dimensional flows of incompressible
  viscoelastic Maxwell medium with upper\, low and corotational convective 
 derivatives in the theological constitutive law are considered. A class of
  partially invariant solutions is analyzed. Using transition to Lagrangian
  coordinates\, an exact solution of the problem of unsteady flow near free
 -stagnation point was constructed. For the model with Johnson-Segalman con
 vected derivative and special linear dependence of the vertical component 
 of velocity\, the general solution was derived. Analysis of the analytical
  unstationary solution provides a new class of stationary solutions. The s
 olutions found comprise both already known as well as substantially new so
 lutions. Nonsingular solutions of the stress tensor at the critical point 
 and bounded at infinity are constructed. Exact analytical formulae for the
  stress tensor with the Weissenberg number Wi=1/2 are obtained.\n\nZoom li
 nk: https://us04web.zoom.us/j/75235003172?pwd=MXpVbGlLN0ZGQ1NpTVErV2xvLzFB
 dz09\n
LOCATION:https://researchseminars.org/talk/mmandim/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karima Khusnutdinova (University Loughborough)
DTSTART:20200610T110000Z
DTEND:20200610T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/3/">
 Near-integrable models for long surface and internal ring waves in stratif
 ied shear flows</a>\nby Karima Khusnutdinova (University Loughborough) as 
 part of Mathematical models and integration methods\n\n\nAbstract\nIn this
  talk I will first overview some general results concerning the effects of
  the parallel shear flow on long weakly-nonlinear surface and internal rin
 g waves in a stratified fluid (e.g.\, oceanic internal waves generated in 
 narrow straits and river-sea interaction zones)\, generalising the results
  for surface waves in a homogeneous fluid [1]. We showed that despite the 
 clashing geometries of the waves and the shear flow\, there exists a linea
 r modal decomposition (separation of variables) in the far-field set of Eu
 ler equations describing the waves in a stratified fluid\, more complicate
 d than the known decomposition for plane waves [2\,3]. We used it to descr
 ibe the wavefronts of surface and internal waves\, and to derive a 2D cyli
 ndrical Korteweg - de Vries (cKdV)-type model for the amplitudes of the wa
 ves. The distortion of the wavefronts is described explicitly by construct
 ing the singular solution (envelope of the general solution) of a respecti
 ve nonlinear first-order differential equation. \n\nNext\, we consider a t
 wo-layer fluid with a rather general depth-dependent upper-layer current (
 e.g. a river inflow\, or a wind-generated current). In the rigid-lid appro
 ximation\, we find the necessary singular solution of the nonlinear first-
 order ordinary differential equation responsible for the adjustment of the
  speed of the long interfacial ring wave in different directions in terms 
 of the hypergeometric function [4]. This allows us to obtain an analytical
  description of the wavefronts and vertical structure of the ring waves fo
 r a large family of the current profiles and to illustrate their dependenc
 e on the  density jump and the type and the strength of the current. We wi
 ll also discuss a 2D generalisation of the long-wave instability criterion
  for plane interfacial waves on a piecewise-constant current [4]\, which o
 n physical level manifests itself in the counter-intuitive squeezing of th
 e wavefront of the interfacial ring wave.\n\nREFERENCES\n\n1. R.S. Johnson
 \, Ring waves on the surface of shear flows: a linear and nonlinear theory
 \, J. Fluid Mech.\, 215\, 1638-1660 (1990).\n\n2. K.R. Khusnutdinova\, X. 
 Zhang\, Long ring waves in a stratified fluid over a shear flow\, J. Fluid
  Mech.\, 794\, 17-44 (2016).\n\n3. K.R. Khusnutdinova\, X. Zhang\, Nonline
 ar ring waves in a two-layer fluid\, Physica D\, 333\, 208-221 (2016).\n\n
 4. K.R. Khusnutdinova\, Long internal ring waves in a two-layer fluid with
  an upper-layer current\, submitted (2020). \n\n5. L.V. Ovsyannikov\, Two-
 layer 'shallow water' model\, J. Appl. Math. Tech. Phys. 20\, 127-135 (197
 9).\n\nZoom limk: https://us04web.zoom.us/j/75476385312?pwd=dTU0U0VQMTN5Vl
 FOMVVHNmhaS1pCZz09\n
LOCATION:https://researchseminars.org/talk/mmandim/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey P. Tsarev (Siberian Federal University\, Krasnoyarsk\, Russ
 ia)
DTSTART:20200617T110000Z
DTEND:20200617T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/4/">
 Free interpolation of GLONASS/GPS orbits: solving a two-point boundary-val
 ue problem without solving differential equations</a>\nby Sergey P. Tsarev
  (Siberian Federal University\, Krasnoyarsk\, Russia) as part of Mathemati
 cal models and integration methods\n\n\nAbstract\nThis talk will give a to
 tally different view to the problem addressed in my previous talk\n\n"Disc
 rete orthogonal polynomials: anomalies of time series and boundary effects
  of polynomial filters". \n\nUsing a sort of adaptive filtering we solve t
 he problem of boundary attenuation effects of polynomial filters. The tech
 niques we use may be classified as (elementary) machine learning.\n\nAnoth
 er facet of the GNSS (Global Navigation Satellite Systems) theory and prac
 tice exposed in this talk is the problem of interpolation of positions of 
 GNSS satellites.\nUsing the data from IGS (International GNSS Service) as 
 an example\, we demonstrate a simple but unexpectedly effective technique 
 that allows interpolation of the positions of GPS and GLONASS satellites w
 ith an accuracy of a few millimeters. It is natural to call the described 
 interpolation technique "free" since it is not related to polynomials\, no
 r trigonometric and other functions commonly used in standard interpolatio
 n techniques.\n\nThe free interpolation technique also allows developing m
 uch more accurate (nevertheless very simple) models of media that are impo
 rtant in the operation of space navigation systems: the ionosphere\, tropo
 sphere\, etc.\n\nThe basis for the development of this method is Big Data\
 , accumulated over many years of operation of satellite navigation systems
 . We will discuss some common problems of the Big Data we use. The followi
 ng conclusion turned out to be paradoxical\, but real: the main problem wh
 en working with big data is that there are too few of them...\n\nThis talk
  is a modified version of my Russian language talk given in 2018:\nhttp://
 www.mathnet.ru/php/presentation.phtml?&presentid=24129&option_lang=eng\n\n
 Paper references:\n\n1. Pustoshilov\, A. S.\, & Tsarev\, S. P. (2017). Uni
 versal coefficients for precise interpolation of GNSS orbits from final IG
 S SP3 data. In 2017 International Siberian Conference on Control and Commu
 nications (SIBCON) (pp. 1-6). IEEE. https://ieeexplore.ieee.org/abstract/d
 ocument/7998463\n\n2. Pustoshilov\, A. S.\, & Tsarev\, S. P. (2018). Two-p
 oint free nonlinear interpolation of coordinates and velocities of navigat
 ion satellites from SP3 data. (in Russian) Achievements of Modern Radioele
 ctronics / №12 - 2018 http://www.radiotec.ru/article/22602#english\n\n3.
  Tsarev\, S. P.\, Denisenko\, V. V.\, & Valikhanov\, M. M. (2018). Multidi
 mensional free interpolation framework for high-precision modeling of slan
 t total electron contents in mid-latitude and equatorial regions. http://e
 lib.sfu-kras.ru/handle/2311/109067?locale-attribute=en\n\nZoom link: \nhtt
 ps://us04web.zoom.us/j/2084211239?pwd=bzZoZFF0RFl6TzBBZ2hHa3pZS0prQT09\n
LOCATION:https://researchseminars.org/talk/mmandim/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey V. Shmidt (Institute of Computational Modelling SB RAS\, Kr
 asnoyarsk\, Russia)
DTSTART:20200624T110000Z
DTEND:20200624T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/5/">
 On self-similar solutions for some problems of free turbulence</a>\nby Ale
 xey V. Shmidt (Institute of Computational Modelling SB RAS\, Krasnoyarsk\,
  Russia) as part of Mathematical models and integration methods\n\n\nAbstr
 act\nThree-dimensional far turbulent wake in a passive stratified medium\,
 \naxisymmrtric submerged turbulent jet and far swirling turbulent wake are
  considered using RANS approach.\n\nWe use methods of a group-theoretical 
 analisys to reduce corresponding semi-emprirical models of turbulence\nto 
 systems of ordinary differential equations (ODEs). Modified shooting metho
 d and asymptotic expansion are used\n to solve boundary-value problems for
  obtained systems of ODEs. The constructed solutions are in good agreement
  with\n experimental data. Moreover\, a detailed comparison with numerical
  solutions obtained by G.G. Chernykh with co-authors\n on the basis of the
  full models of turbulence were conducted.\n\nKaptsov O.V.\, Shmidt A.V. A
  three-dimensional semi-empirical model of a far turbulent wake // J. Appl
 . Math. Mech.\, 2015\, V. 79\, № 5\, P. 459-466\n\nShmidt A.V. Self-Simi
 lar solution of the problem of a turbulent flow in a round submerged jet /
 / J. of Appl. Mech. and Tech. Phys.\, 2015\, V. 56\, № 3\, P. 414-419\n\
 nShmidt A.V. Similarity in the far swirling momentumless turbulent wake //
  J. SFU. Math. & Phys.\, 2020\, V. 13\, № 1\, P. 79-86\n\nНа осно
 ве подхода RANS рассмотрены трехмерный да
 льний турбулентный след в пассивно-стра
 тифицированной среде\,\nосесимметричная 
 затопленная турбулентная струя и дальни
 й закрученный турбулентный след.\nС помо
 щью методов теоретико-группового анализ
 а соответствующие полуэмпирические мод
 ели турбулентности редуцируются\n к сист
 емам обыкновенных дифференциальных ура
 внений. Поставленные краевые задачи для 
 систем обыкновенных дифференциальных\n 
 уравнений решены с использованием модиф
 ицированного метода стрельбы и асимптот
 ического разложения решения\n в окрестно
 сти особой точки. Построенные решения на
 ходятся в хорошем согласии с эксперимен
 тальными данными.\n Кроме того\, было пров
 едено детальное сопоставление с численн
 ыми решениями\, полученными Г.Г. Черных с 
 соавторами\n на основе полных моделей ту
 рбулентности.\n\nPlease join Zoom channel with your real name!
 \n
LOCATION:https://researchseminars.org/talk/mmandim/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan G. Dimitrov (Institute of Nuclear Research and Nuclear Ener
 getics (INRNE))
DTSTART:20200701T110000Z
DTEND:20200701T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/6/">
 Applied General Theory of Relativity: Physical Principles of the Global Po
 sitioning System (GPS)</a>\nby Bogdan G. Dimitrov (Institute of Nuclear Re
 search and Nuclear Energetics (INRNE)) as part of Mathematical models and 
 integration methods\n\n\nAbstract\n(The talk will be given in Russian with
  English slides)\n\nПрикладная Общая Теория Отно
 сительности: физические принципы Глобал
 ьной Системы Позиционирования (GPS)\n\nZoom lin
 k:\nhttps://us04web.zoom.us/j/2084211239?pwd=bzZoZFF0RFl6TzBBZ2hHa3pZS0prQ
 T09\n\nA general knowledge about the fundamental physical principles of th
 e Global Positioning System (GPS) will be presented. One of these principl
 es is related to the fundamental fact (the Michelson-Morley experiment) ab
 out the independence of the velocity of light from the velocity of the sou
 rce of light and the non-existence of “ether”\, which was the starting
  point for the creation of the Special Theory of Relativity by Albert Eins
 tein. Particular attention will be paid to some (elementary) model example
 s\, resulting in important relations\, concerning the frequency change of 
 the signal between the stations on the Earth’s surface and the rotating 
 satellites around the Earth. This frequency change depends on the rotation
  of the Earth\, as well as on the variation of the gravitational potential
 . The amazing relation of these dependencies to the approach of Special Th
 eory of Relativity will be demonstrated\, also the further extension of th
 e approach in the framework of the General Theory of Relativity\, which is
  being applied in the theory of the Global Positioning System since 2003.\
 n  The Geocentric Relativistic Reference System will be briefly reviewed\,
  also the determination of the atomic clock times with respect to an attac
 hed to the Earth rotating coordinate system\, which is important for takin
 g into account the General Relativity Theory effects during the satellite 
 motion in the near-Earth space.\n   \n   REFERENCES\n1.	Neil Ashby\, Relat
 ivistic effects in the Global Positioning System\, in Gravitation and Rela
 tivity at the Turn of the Millenium\, Proceedings of the 15th Internationa
 l Conference on General Relativity and Gravitation\, edited by N.Dadhich a
 nd J. Narlikar (International University Centre for Astronomy and Astrophy
 sics\, 1998).\n\n2.	N. Ashby\, Relativity in the Global Positioning System
 \, Living Reviews in Relativity 6\, 1-42 (2003)\, https://link.springer.co
 m/content/pdf/10.12942%2Flrr-2003-1.pdf.\n\n3.	N. Ashby\, and R. A. Nelson
 \, in Relativity in Fundamental Astronomy: Dynamics\, Reference Frames\, a
 nd Data Analysis\, Proceedings of the IAU Symposium 261 2009\, edited by S
 . A. Klioner\, P. K. Seidelmann\, and M. H.Soffel (Cambridge University Pr
 ess\, Cambridge\, 2010).\n\n4.	J. - F. Pascual Sanchez\, Introducing Relat
 ivity in Global Navigation Satellite System\, Ann. Phys. (Leipzig) 16\, 25
 8-273 (2007).\n\n5.	Michael H. Soffel\, and Wen-Biao Han\, Applied General
  Relativity. Theory and Applications in Astronomy\, Celestial Mechanics an
 d Metrology\, Springer Nature\, Switzerland AG 2019.\n\n6.	Michael H. Soff
 el\, and R. Langhans\, Space-Time Reference Systems (Springer-Verlag\, Ber
 lin Heidelberg\, 2013 ).\n\n7.	Sergei M. Kopeikin\, Michael Efroimsky\, an
 d George Kaplan\, Relativistic Celestial Mechanics of the Solar System (Wi
 ley-VCH\, New York\, 2011).\n\n8.	L. Duchayne\, Transfert de temps de haut
 e performance: le Lien Micro-Onde de la mission ACES. Physique mathematiqu
 e [math-ph]. PhD Thesis\, Observatoire de Paris\, 2008. Francais\, HAL Id:
  tel-00349882\, https://tel.archives-ouvertes.fr/tel-00349882/document.\n\
 n9.	M. Gulklett\, Relativistic effects in GPS and LEO\, October 8 2003\, P
 hD Thesis\, University of Copenhagen\, Denmark\, Department of Geophysics\
 , The Niels Bohr Institute for Physics\, Astronomy and Geophysics\, availa
 ble at https://www.yumpu.com/en/document/view/4706552/relativistic-e_ects-
 in-gps-and-leo-niels-bohr-institutet.\n\n10.	 B. Hofmann-Wellenhof\, and H
 . Moritz\, Physical Geodesy (Springer-Verlag\, Wien-New York\, 2005).\n\n1
 1.	Slava G. Turyshev\, Viktor T. Toth\, and Mikhail V. Sazhin\, General re
 lativistic observables of the GRAIL mission\, Phys. Rev. D87\, 024020 (201
 3)\, arXiv:1212.0232v4 [gr-qc].\n\n12.	Slava G. Turyshev\, Mikhail V. Sazh
 in\, and Viktor T. Toth\, General relativistic laser interferometric obser
 vables of the GRACE-Follow-On mission\, Phys. Rev. D89\, 105029 (2014)\, a
 rXiv: 1402.7111v1 [qr-qc].\n\n13.	Slava G. Turyshev\, Nan Yu\, and Viktor 
 T. Toth\, General relativistic observables for the ACES experiment\, Phys.
  Rev. D93\, 045027 (2016)\, arXiv: 1512.09019v2 [gr-qc].\n\n14.	R. A. Nels
 on\, Relativistic time transfer in the vicinity of the Earth and in the So
 lar system\, Metrologia 48\, S171 (2011).\n\n15.	Bogdan G. Dimitrov\, the 
 (third) extended version of arXiv:1712.01101 [gr-qc] (contains a lot of re
 ferences).\n\n16.	Bogdan G. Dimitrov\, New Mathematical Models of GPS Inte
 rsatellite Communications in the Gravitational Field of the Near-Earth Spa
 ce\, AIP Confer. Proc. 2075\, 040007 (2019)\; https://doi.org/10.1063/1.50
 91167.\n\n\nБудут представлены некоторые осн
 овные сведения о фундаментальных физиче
 ских принципах\, на которых основано фун
 кционирование Глобальной Системы Позиц
 ионирования (GPS). Один из этих принципов и
 меет связь с фундаментальным фактом о не
 зависимости скорости света от скорости 
 источника (эксперимент Майкельсона-Морл
 и) и несуществования т.н. «эфира»\, которо
 й являлся отправной точкой для построен
 ии Специальной Теории Относительности (
 СТО) Альбертом Эйнштейном. Особое вниман
 ие будет уделено некоторыми (элементарн
 ыми) модельными примерами\, на основе кот
 орых выводятся важные зависимости о час
 тотном изменении сигнала\, посылаемым ст
 анциями на Земле к спутникам (и обратно). 
 Эта частота зависит от угловой скорости 
 вращения Земли\, а также от изменения гра
 витационного потенциала. Будет продемон
 стрировано удивительное согласование э
 тих зависимостей с подходами Специально
 й Теории Относительности\, а также дальн
 ейшее расширение подхода в рамках Общей 
 Теории Относительности (ОТО)\, которая пр
 именяется в теории GPS после 2003-го года.\n  
 Коротко будет рассмотрена Геоцентричес
 кая Релятивистская Система Отсчета и оп
 ределение времени атомных часов относит
 ельно вращающейся вместе со Землей коор
 динатной системой. Время\, которое указы
 вают эти часы\, существенно для исследов
 ания эффектов ОТО при движении спутнико
 в в пространстве вокруг Земли.\n
LOCATION:https://researchseminars.org/talk/mmandim/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan G. Dimitrov (Institute of Nuclear Research and Nuclear Ener
 getics (INRNE))
DTSTART:20200708T110000Z
DTEND:20200708T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/7/">
 Intersecting Null Cones and GPS\, GLONASS Intersatellite Communications in
  the Gravitational Field of Near-Earth Space with Account of General Relat
 ivity Theory</a>\nby Bogdan G. Dimitrov (Institute of Nuclear Research and
  Nuclear Energetics (INRNE)) as part of Mathematical models and integratio
 n methods\n\n\nAbstract\n(The talk will be given in Russian with English s
 lides)\n\nZoom link: https://us04web.zoom.us/j/2084211239?pwd=bzZoZFF0RFl6
 TzBBZ2hHa3pZS0prQT09\n\nПересекающиеся нулевые кон
 усы межспутниковых коммуникаций для GPS и
  GLONASS в гравитационном поле околоземного
  пространства с учетом эффектов Общей Те
 ории Относительности\n\nIn this report a theoretical ap
 proach will be presented for intersatellite communications (ISC) between t
 wo satellites (belonging to satellite configurations GPS or GLONASS)\, mov
 ing on (one-plane) elliptical orbits. The new approach is based on the int
 roduction of two null cones with origins at the emitting-signal and receiv
 ing-signal satellites. The two null cones (intersected also with a hyperpl
 ane) account for the variable distance between the satellites. This inters
 ection of the two null cones gives the space-time interval in GRT. Applyin
 g some theorems from higher algebra\, it was proved that this space-time d
 istance can become zero\, consequently it can be also negative and positiv
 e. But in order to represent the geodesic distance travelled by the signal
 \, the space-time interval has to be "compatible" with the Euclidean dista
 nce. So this "compatibility condition"\, conditionally called "condition f
 or ISC"\, is the most important consequence of the theory. The other impor
 tant consequence is that the geodesic distance turns out to be the space-t
 ime interval\, but with account also of the "condition for ISC". The geode
 sic distance turns out to be greater than the Euclidean distance - a resul
 t\, entirely based on the "two null cones approach" and moreover\, without
  any use of the Shapiro delay formulae. Application of the same higher alg
 ebra theorems shows that the geodesic distance cannot have any zeroes\, in
  accord with being greater than the Euclidean distance. The theory also pu
 ts a restriction on the eccentric anomaly angle E=45.00251 [deg]\, which i
 s surprisingly close to the angle of disposition of the satellites in the 
 GLONASS satellite constellation - 8 satellites within one and the same pla
 ne equally spaced at 45 deg. Under some specific restrictions and for the 
 case of plane motion of the satellites\, an analytical formula was derived
  for the propagation time of the signal\, emitted by a moving along an ell
 iptical orbit satellite. The formula can be represented as a sum of ellipt
 ic integrals of the first\, second and the third kind. \n\nReferences\n\n1
 . Bogdan G. Dimitrov\, Two null gravitational cones in the theory of GPS-i
 ntersatellite communications between two moving satellites. I. Physical an
 d mathematical theory of the space-time interval and the geodesic distance
  on intersecting null cones\, (third) extended version of https://arxiv.or
 g/abs/1712.01101v3 [gr-qc]\, 162 pages .\n\n2. Bogdan G. Dimitrov\, New Ma
 thematical Models of GPS Intersatellite Communications in the Gravitationa
 l Field of the Near-Earth Space\, AIP Confer. Proc. 2075\, 040007 (2019)\;
  https://doi.org/10.1063/1.5091167 \, 9 pages. \n\nВ этом докла
 де будет представлен теоретический подх
 од для спутниковых коммуникаций между д
 вумя спутниками (GPS\, GLONASS)\, которые двига
 ются по эллиптических орбитах. Подход ос
 нован на введении двух нулевых конусов с
  вершинами в спутниках\, посылающие и при
 нимающие сигналы соответственно. Два ну
 левых конуса (пересекающихся также с гип
 ерплоскостью) учитывают изменяющееся ра
 сстояние между спутниками. Пересечение 
 двух нулевых конусов задает пространств
 енно-временной интервал в ОТО. Применяя 
 некоторые теоремы из высшей алгеброй\, б
 ыло показано\, что пространственно-време
 нной интервал может равняться нулю\, сле
 довательно он может быть также и отрицат
 ельным\, и положительным. Но чтобы этот и
 нтервал представлял геодезическое расс
 тояние\, пространственно-временной инте
 рвал должен быть «согласованным» со Евк
 лидовым расстоянием. Таким образом\, это 
 «условие согласованности»\, условно наз
 ванное «условие для спутниковых коммуни
 каций»\, является наиболее важным следст
 вием теории. Другое важное следствие: ге
 одезическое расстояние оказывается про
 странственно-временным интервалом\, но с
  учетом «условия для спутниковых коммун
 икаций». Таким образом\, геодезическое р
 асстояние оказывается большим\, чем Евкл
 идово расстояние – результат\, которой о
 сновывается только на «подходе двух кон
 усов» и более того\, без использования фо
 рмулы Шапиро для замедления сигнала. При
 менение этих же теорем из высшей алгебро
 й показывает\, что геодезическое расстоя
 ние не имеет никаких нулей\, в соответств
 ии с тем\, что оно больше евклидова расст
 ояния. Теория также накладывает огранич
 ение на угол эксцентричной аномалии E=45.00
 251 [deg]\, что удивительно близко к угловому
  расстоянию спутников в конфигурации ГЛ
 ОНАСС (российский аналог американского G
 PS) - 8 спутников в одной и той же плоскости
  с равным интервалом в 45 градусов. При не
 которых конкретных ограничениях и для с
 лучая плоского движения спутников\, анал
 итическая формула была получена для вре
 мени распространения сигнала\, излучаем
 ым движущимся по эллиптической орбите с
 путником. Формула может быть представле
 на в виде суммы эллиптических интеграло
 в первого\, второго и третьего рода.\n
LOCATION:https://researchseminars.org/talk/mmandim/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Shlapunov (Siberian Federal University\, Krasnoyarsk\, R
 ussia)
DTSTART:20201009T110000Z
DTEND:20201009T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/8/">
 Existence Theorems for Regular Spatially Periodic Solutions to the Navier
 –Stokes Equations in R^3</a>\nby Alexander Shlapunov (Siberian Federal U
 niversity\, Krasnoyarsk\, Russia) as part of Mathematical models and integ
 ration methods\n\n\nAbstract\nWe consider the initial problem for the Navi
 er–Stokes equations over ${\\mathbb R}^3 \\times [0\,T]$ with a positive
  time $T$ in the spatially periodic setting. Identifying periodic vector-v
 alued functions on ${\\mathbb R}^3$ with functions on the $3\\\,$-dimensio
 nal torus ${\\mathbb T}^3$\, we prove that the problem induces an open bot
 h injective and surjective mapping of specially constructed scale of funct
 ion spaces of Bochner–Sobolev type parametrised with the smoothness inde
 x $s\\in \\mathbb{N}$. The intersection of these classes with respect $s$ 
 gives a uniqueness and existence theorem for smooth solutions to the Navie
 r–Stokes equations for each finite $T>0$. Then additional intersection w
 ith respect to $T\\in (0\, +\\infty)$ leads to a uniqueness and existence 
 theorem for smooth solutions and data having prescribed asymptotic behavio
 ur at the infinity with respect to the time variable. Actually\, we propos
 e the following modified scheme of the proof of the existence theorem\, ba
 sed on apriori estimates and operator approach in Banach spaces:\n\n1. We 
 prove that the Navier–Stokes equations induce continuous injective OPEN 
 mapping between the chosen Banach spaces.\n\n2. Next\, the standard topolo
 gical arguments immediately imply that a nonempty open connected set in a 
 topological vector space coincides with the space itself if and only if th
 e set is closed. This reduces the proof of the existence theorem to an $L^
 \\mathfrak{s} ([0\,T]\, L^\\mathfrak{r} ({\\mathbb R^3}))$ a priori estima
 te for the INVERSE IMAGE OF PRECOMPACT SETS in the target Banach space whe
 re $\\mathfrak{s}$\, $\\mathfrak{r}$ are Ladyzhenskaya–Prodi–Serrin nu
 mbers satisfying $2/\\mathfrak{s} + 3/\\mathfrak{r} = 1$ and $\\mathfrak{r
 } > 3$. In this way we avoid proving a GLOBAL $L^\\mathfrak{s} ([0\,T]\, L
 ^\\mathfrak{r} ({\\mathbb R^3}))$ a priori estimate.\n\n3. To prove the we
 ak $L^\\mathfrak{s} ([0\,T]\, L^\\mathfrak{r} ({\\mathbb R^3}))$ a priori 
 estimate with $\\mathfrak{r} > 3$ we calculate precisely the excess betwee
 n the left hand side and the right hand side of the corresponding energy i
 nequality\, that equals to $2r$ when expressed in terms of the Lebesgue in
 tegrability index $r$. Then we operate with absolutely convergent series i
 nvolving Lebesgue norms that gives the possibility to group together summa
 nds in a suitable way\, using the energy type inequalities\, interpolation
  inequalities and matching the asymptotic behaviour in order to exclude th
 e unbounded sequences in the inverse image of a precompact set.\n
LOCATION:https://researchseminars.org/talk/mmandim/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg V. Kaptsov (Institute of Computational Modeling SB RAS)
DTSTART:20201023T110000Z
DTEND:20201023T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/9/">
 Exact Solution of Boussinesq equations for propagation of nonlinear waves<
 /a>\nby Oleg V. Kaptsov (Institute of Computational Modeling SB RAS) as pa
 rt of Mathematical models and integration methods\n\n\nAbstract\nIn this p
 aper\, we consider two Boussinesq models that describe propagation of smal
 l-amplitude long water waves. Exact solutions of the classical Boussinesq 
 equation that represent the interaction of wave packets and waves on solit
 ons are found. We use the Hirota representation and computer algebra metho
 ds. Moreover\, we find various solutions for one of the variants of the Bo
 ussinesq system. In particular\, these solutions can be interpreted as the
  fusion and decay of solitary waves\, as well as the interaction of more c
 omplex structures.\n
LOCATION:https://researchseminars.org/talk/mmandim/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg V. Kaptsov (Institute of Computational Modeling SB RAS)
DTSTART:20201106T110000Z
DTEND:20201106T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/10/"
 >Iterations and groups of formal transformations</a>\nby Oleg V. Kaptsov (
 Institute of Computational Modeling SB RAS) as part of Mathematical models
  and integration methods\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/mmandim/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А. Е. Миронов (Институт математики им
 . С. Л. Соболева СО РАН)
DTSTART:20201113T110000Z
DTEND:20201113T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/11/"
 >Интегрируемые магнитные геодезические 
 потоки на двумерном торе и системы гидро
 динамического типа</a>\nby А. Е. Миронов (Инс
 титут математики им. С. Л. Соболева СО РАН
 ) as part of Mathematical models and integration methods\n\nAbstract: TBA\
 n
LOCATION:https://researchseminars.org/talk/mmandim/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А. Е. Миронов (Институт математики им
 . С. Л. Соболева СО РАН)
DTSTART:20201127T110000Z
DTEND:20201127T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/12/"
 >Коммутирующие разностные операторы</a>\nb
 y А. Е. Миронов (Институт математики им. С. 
 Л. Соболева СО РАН) as part of Mathematical models and integ
 ration methods\n\n\nAbstract\nВ докладе будет рассказ
 ано о задаче построения коммутативных к
 олец разностных операторов. С помощью од
 ноточечных коммутирующих разностных оп
 ераторов ранга один будет построена дис
 кретизация оператора Ламе.\n
LOCATION:https://researchseminars.org/talk/mmandim/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:E. I. Kaptsov (Keldysh Institute of Applied Mathematics of Russian
  Academy of Science)
DTSTART:20201211T110000Z
DTEND:20201211T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/13/"
 >Invariant finite-difference schemes for equations of continuous medium po
 ssessing finite-difference conservation laws</a>\nby E. I. Kaptsov (Keldys
 h Institute of Applied Mathematics of Russian Academy of Science) as part 
 of Mathematical models and integration methods\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/mmandim/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Shlapunov (Siberian Federal University\, Krasnoyarsk\, R
 ussia)
DTSTART:20201225T110000Z
DTEND:20201225T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/14/"
 >Existence theorems for regular solutions to the Cauchy problem for the Na
 vier-Stokes equations in R^3</a>\nby Alexander Shlapunov (Siberian Federal
  University\, Krasnoyarsk\, Russia) as part of Mathematical models and int
 egration methods\n\n\nAbstract\nWe consider the Cauchy problem for the Nav
 ier-Stokes equations over ${\\mathbb R}^3 \\times [0\,T]$ with a positive 
 time $T$ over a specially constructed scale of function spaces of Bochner-
 Sobolev type. We prove that the problem induces an open both injective and
  surjective mapping of each space of the scale. In particular\, intersecti
 on of these classes gives a uniqueness and existence theorem for smooth so
 lutions to the Navier-Stokes equations for smooth data with a prescribed a
 symptotic behaviour at the infinity with respect to the time and the space
  variables. Actually\, we propose the following modified scheme of the pro
 of of the existence theorem\, based on apriori estimates and operator appr
 oach in Banach spaces:\n\n1. We prove that the Navier-Stokes equations ind
 uce continuous injective OPEN mapping between the chosen Banach spaces.\n\
 n2. Next\, the standard topological arguments immediately imply that a non
 empty open connected set in a topological vector space coincides with the 
 space itself if and only if the set is closed. This reduces the proof of t
 he existence theorem to an $L^\\mathfrak{s} ([0\,T]\, L^\\mathfrak{r} ({\\
 mathbb R^3}))$ a priori estimate for the INVERSE IMAGE OF PRECOMPACT SETS 
 in the target Banach space where $\\mathfrak{s}$\, $\\mathfrak{s}$ are Lad
 yzhenskaya-Prodi-Serrin numbers satisfying $2/\\mathfrak{s} + 3/\\mathfrak
 {r} = 1$ and $\\mathfrak{r} > 3$. In this way we avoid proving a GLOBAL $L
 ^\\mathfrak{s} ([0\,T]\, L^\\mathfrak{r} ({\\mathbb R^3}))$ a priori estim
 ate.\n\n3. To prove the weak $L^\\mathfrak{s} ([0\,T]\, L^\\mathfrak{r} ({
 \\mathbb R^3}))$ a priori estimate with $\\mathfrak{r} > 3$ we calculate p
 recisely the excess between the left hand side and the right hand side of 
 the corresponding energy inequality\, that equals to $2r$ when expressed i
 n terms of the Lebesgue integrability index $r$. Then we operate with abso
 lutely convergent series involving Lebesgue norms that gives the possibili
 ty to group together summands in a suitable way\, using the energy type in
 equalities\, interpolation inequalities and matching the asymptotic behavi
 our in order to exclude the unbounded sequences in the inverse image of a 
 precompact set.\n\nAn early version of the paper is uploaded on arxiv.org:
  https://arxiv.org/abs/2009.10530\nA similar approach can be used for inve
 stigation of the Navier-Stokes equations in the periodic setting: https://
 arxiv.org/abs/2007.14911\n
LOCATION:https://researchseminars.org/talk/mmandim/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.N. Rogalev (Institute of Computational Modeling SB RAS)
DTSTART:20210204T110000Z
DTEND:20210204T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/15/"
 >Regularization of numerical estimation of the sets of solutions of ODEs  
 in stability problems on a finite time interval</a>\nby A.N. Rogalev (Inst
 itute of Computational Modeling SB RAS) as part of Mathematical models and
  integration methods\n\n\nAbstract\nThe sets of ODE solutions\, with initi
 al data belonging to the initial data regions\, have complex boundaries (b
 oundary surfaces in the dimension space). For the boundaries of the sets o
 f solutions (surfaces in the space of solutions)\, it is impossible to cho
 ose formulas of functions with the help of which it was possible to descri
 be the boundaries. As a result\, there are two possibilities — either to
  describe the values of the boundary surfaces in a set of discrete points 
 (on a grid)\, or to calculate their estimates of the maximum values in the
  directions of the coordinate axes\, or the maximum in any chosen directio
 n. The paper investigates and further uses the injectivity property of sol
 utions to ODEs. For linear systems of ODEs  the shift operator is linear a
 nd monomorphic (i.e.\, injective). These properties are also possessed by 
 the resolving operator\, which associates with the initial value the solut
 ion of the corresponding Cauchy problem (the entire solution\, not its val
 ue at a point) as an element of space.\n\nFor nonlinear ODE systems that h
 ave unique solutions in a certain region of initial data\, the boundaries 
 of the regions of initial data pass into the boundaries of the regions of 
 solutions at each specific moment in time. The class of such nonlinear ODE
  systems consists of systems whose solutions are uniformly bounded (Lagran
 ge stable). Preliminarily\, it is useful to construct a regularization of 
 estimates for the boundaries of the solution sets\, passing to the linear 
 approximation of the original system. Regularization is understood as find
 ing information about sets of exact solutions. This regularization establi
 shes  the values of compression / expansion in the given directions\, offs
 et along the time axis\, and rotation through some angle. Examples of stab
 ility studies on a finite time interval are given.\n
LOCATION:https://researchseminars.org/talk/mmandim/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.V. Aksenov
DTSTART:20210218T110000Z
DTEND:20210218T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/16/"
 >Symmetries\, conservation laws\, and exact solutions to a one-dimensional
  system of shallow water equations over an uneven bottom</a>\nby A.V. Akse
 nov as part of Mathematical models and integration methods\n\n\nAbstract\n
 The symmetries of a one-dimensional system of shallow water equations over
  an uneven bottom in Euler’s variables are classified. Based on the resu
 lts of the group classification obtained\, it is concluded that it is poss
 ible to reduce the one-dimensional system of shallow water equations to a 
 linear system of equations using point transformations only in the cases o
 f horizontal and inclined bottom profiles. We also classify the contact sy
 mmetries of the one-dimensional shallow water equation over an uneven bott
 om in Lagrangian’s variables.\n\nThe hydrodynamic conservation laws of a
  one-dimensional system of shallow water equations in Eulerian’s variabl
 es are classified. A new basic conservation law is obtained. The first-ord
 er conservation laws of the one-dimensional shallow water equation in Lagr
 angian’s variables are classified.\n\nA three-parameter family of exact 
 solutions of a one-dimensional system of shallow water equations over an i
 nclined bottom is obtained and investigated\, describing the ”step’’
  wave's arrival on the shore and its reflection from it. The nonlinear the
  overwash effect and the effect of the amplification of the incoming wave 
 when it is reflected from the shore are described.\n
LOCATION:https://researchseminars.org/talk/mmandim/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yury Stepanyants (School of Sciences\, University of Southern Quee
 nsland\, Toowoomba\, Australia)
DTSTART:20210311T110000Z
DTEND:20210311T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/17/"
 >The asymptotic approach to the description of two-dimensional soliton pat
 terns in the oceans</a>\nby Yury Stepanyants (School of Sciences\, Univers
 ity of Southern Queensland\, Toowoomba\, Australia) as part of Mathematica
 l models and integration methods\n\n\nAbstract\nThe asymptotic approach is
  suggested for the description of interacting surface and internal oceanic
  solitary waves. This approach allows one to describe a stationary moving 
 wave patterns consisting of two plane solitary waves moving at an angle to
  each other. The results obtained within the approximate asymptotic theory
  is validated by comparison with the exact two-soliton solution of the Kad
 omtsev–Petviashvili equation. The suggested approach is equally applicab
 le to a wide class of non-integrable equations too. As an example\, the as
 ymptotic theory is applied to the description of wave patterns in the 2D B
 enjamin–Ono equation describing internal waves in the infinitely deep oc
 ean containing a relatively thin one of the layers.\n
LOCATION:https://researchseminars.org/talk/mmandim/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Юрий Шанько (Институт вычислительно
 го моделирования СО РАН)
DTSTART:20210325T110000Z
DTEND:20210325T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/18/"
 >Решение задачи  Л.В. Овсянникова о двуме
 рных изотермических движениях политроп
 ного газа</a>\nby Юрий Шанько (Институт вычи
 слительного моделирования СО РАН) as part of 
 Mathematical models and integration methods\n\n\nAbstract\nВ доклад
 е исследуется переопределенная система 
 уравнений в частных производных\n\n$u_t + uu_x
  + vu_y + p_x = 0$\,\n\n$v_t + uv_x + vv_y + p_y = 0$\,\n\n$u_x + v_y = 0\
 ,$ $\\qquad$ $\\qquad$ $\\quad$     (1)\n\n$p_t + up_x + vp_y = 0$\,\n\nя
 вляющаяся двумерным аналогом общей трех
 мерной системы\,\nзадача исследования на 
 совместность которой была поставлена\nв 
 статье Л.В. Овсянникова «О "простых" реше
 ниях уравнений динамики политропного га
 за».\nСистема (1) описывает так называемые
  тепловые (с постоянной плотностью) движ
 ения политропного газа.\nК этой же систем
 е сводятся изотермические (с постоянной 
 скоростью звука) движения газа при показ
 ателе адиабаты не равном $1$.\nВ гидродина
 мике данная система задает двумерные дв
 ижения жидкости с дополнительным услови
 ем постоянства давления в частице.\nЭто у
 словие позволяет интерпретировать кажд
 ое ее решение\, как движение жидкости со 
 свободной границей.\nСистема (1) приведен
 а к пассивному виду и полностью проинтег
 рирована.\n
LOCATION:https://researchseminars.org/talk/mmandim/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:О. В. Капцов (Институт вычислительно
 го моделирования СО РАН)
DTSTART:20210408T110000Z
DTEND:20210408T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/19/"
 >Общие решения некоторых линейных волно
 вых уравнений  с переменными коэффициен
 тами</a>\nby О. В. Капцов (Институт вычислите
 льного моделирования СО РАН) as part of Mathematic
 al models and integration methods\n\n\nAbstract\nВ работе найд
 ены общие решения для некоторых классов 
 линейных волновых уравнений с переменны
 ми коэффициентами. Такие уравнения опис
 ывают колебания стержней\, акустические 
 волны\, а также к ним сводятся некоторые 
 модели газовой динамики. Для построения 
 решений используются преобразования ти
 па Леви\, которые являются дифференциаль
 ными подстановками первого порядка и их 
 итерациями. Приводятся конкретные приме
 ры общих решений\, зависящих от производ
 ных произвольных функций.\n
LOCATION:https://researchseminars.org/talk/mmandim/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.V. Meleshko
DTSTART:20210415T110000Z
DTEND:20210415T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/20/"
 >On generalized simple waves in continuum mechanics</a>\nby S.V. Meleshko 
 as part of Mathematical models and integration methods\n\n\nAbstract\nOne 
 of the well-known classes of solutions of many models of continuum mechani
 cs is a set of solutions called simple wave-type solutions. From the metho
 d of differential constraints point of view\, this class of solutions is d
 escribed by homogeneous differential constraints.  Application of the meth
 od of differential constraints allows one to generalize this class. The ma
 in feature of this class of solutions is that finding a solution of the or
 iginal system of equations is reduced to solving a system of ordinary diff
 erential equations. In particular\, the presentation will show that findin
 g a solution of any Cauchy problem of a homogeneous system of equations wr
 itten in Riemann invariants\, admitting a differential constraint\, is red
 uced to solving the Cauchy problem of system of ordinary differential equa
 tions. This is similar to the method of characteristics for a partial diff
 erential equation with a single dependent variable. Illustrations of solut
 ions for some initial data are given. Several models will be demonstrated 
 in the presentation.\n
LOCATION:https://researchseminars.org/talk/mmandim/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:С.В. Хабиров
DTSTART:20210422T110000Z
DTEND:20210422T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/21/"
 >Стационарная плоская вихревая подмодел
 ь идеального газа</a>\nby С.В. Хабиров as part of 
 Mathematical models and integration methods\n\n\nAbstract\nПодмоде
 ль идеального газа\, инвариантная относи
 тельно переносов по времени и по одному 
 пространственному направлению в случае 
 вихревых движений имеет 4 интеграла. Для 
 функции тока и удельного объема получен
 а система нелинейных дифференциальных у
 равнений 3-го порядка с одним произвольн
 ым элементом\, включающим в себя уравнен
 ие состояния и произвольные функции инт
 егралов. Найдены преобразования эквивал
 ентности по произвольному элементу. Реш
 ена задача групповой классификации. Пол
 учена оптимальная система неподобных по
 далгебр для алгебр из групповой классиф
 икации. Рассмотрены примеры инвариантны
 х решений\, описывающие вихревые движени
 я газа с переменной энтропией\, в том чис
 ле точечный источник или сток. На двумер
 ных подалгебрах получены аналоги просты
 х волн.\n
LOCATION:https://researchseminars.org/talk/mmandim/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Е.Н. Пелиновский (Институт прикладно
 й физики РАН\, Нижний Новгород)
DTSTART:20210513T110000Z
DTEND:20210513T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/22/"
 >Бегущие волны в сильно неоднородных сре
 дах</a>\nby Е.Н. Пелиновский (Институт прикл
 адной физики РАН\, Нижний Новгород) as part of
  Mathematical models and integration methods\n\n\nAbstract\nПод рас
 пространяющейся волной в линейной теори
 и обычно понимает функцию $f(x – ct)$ с прои
 звольной зависимостью от других простра
 нственных координат (здесь $t$ — время\, и 
 $x$ — координата). Их нахождение в случае 
 одной пространственной координаты свод
 ится к решению в простейшем случае систе
 мы обыкновенных дифференциальных уравн
 ений. Более сложно найти бегущие волны в 
 волноводах со сложной поперечной структ
 урой\, и\, например\, нахождение бегущих в
 олн в жидкости со свободной поверхность
 ю стало предметом специального раздела 
 нелинейной математики. Если параметры с
 реды меняются медленно во времени или пл
 авно в пространстве\, то волна локально о
 писывается теми же выражениями\, что и в 
 однородной среде\, а изменение амплитуды
  и фазы волны находится с помощью лучевы
 х методов\, или более строго с помощью ас
 имптотической процедуры. Уже давно было 
 отмечено\, что в некоторых случаях асимп
 тотические решения являются точными и н
 е требуют плавности изменения параметро
 в среды. При этом возникают вопросы\, явл
 яются ли такие решения бегущими волнами\
 , если среда не является плавно неодноро
 дной. В настоящем докладе эта проблема о
 бсуждается применительно к волнам на во
 де. Показывается\, что существуют нескол
 ько профилей переменной глубины\, когда 
 асимптотические решения для линейных во
 лн становятся точными решениями. Такие р
 ешения всегда имеют сингулярные точки. Н
 аряду с монохроматическими волнами\, пол
 учены решения в виде бегущих импульсов\, 
 и исследована их форма. В частности\, для 
 одного класса донной геометрии поверхно
 стная волна должна быть знакопеременной
 \, при этом волна скорости частиц меняет 
 свою форму по мере распространения. Полу
 чены соответствующие решения начальной 
 задачи\, демонстрирующие особенности фо
 рмирования бегущих волн\, движущихся в п
 ротивоположных направлениях\, при этом в
  общем случае формируется зона переменн
 ого течения между двумя разбегающими во
 лнами. Эти решения применяются для изуче
 ния трансформации и отражения волны от и
 злома глубины. Несмотря на «точечность» 
 отражения\, форма отраженной и преломлен
 ной волны меняется кардинально\, в частн
 ости для любой формы падающей волны\, тра
 нсформированная волна является знакопе
 ременной. Приводятся примеры бегущих во
 лн в атмосферной акустике\, солнечной ат
 мосфере и физики внутренних волн в страт
 ифицированной жидкости. Существенно мен
 ьше результатов получено в нелинейной з
 адаче.\n
LOCATION:https://researchseminars.org/talk/mmandim/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.A. Talyshev
DTSTART:20210520T110000Z
DTEND:20210520T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/23/"
 >On the Lifetime of a Free Neutron</a>\nby A.A. Talyshev as part of Mathem
 atical models and integration methods\n\n\nAbstract\nDetermination of the 
 lifetime of a free neutron by the beam method and the 'bottled' method giv
 e aloud different values [1]\, [2]. And this difference has not yet been e
 xplained by insufficient accuracy methods\, no relativistic correction.\nI
 n the beam method neutrons move at a speed of about 10000 km/sec\, and in 
 the 'bottled' method is much slower. On the other hand\, we can constructi
 ng coordinate transformations inertial frames of reference abandoning the 
 direct comparing moving and stationary objects and from the assumption abo
 ut the finiteness of the speed of light [3]. These transformations lead to
  the maximum speed. And with a certain agreement on the choice of bases co
 incide with the Lorentz transformations (if we take this limiting speed fo
 r the speed of light). In this case\, the correction for time dilation doe
 s not have to coincide with the generally accepted in the special theory o
 f relativity.\n\n1. A. T. Yue\, M. S. Dewey\, D. M. Gilliam\, G. L. Greene
 \, A. B. Laptev\, J. S. Nico\, W. M. Snow\, and F. E. Wietfeldt Improved D
 etermination of the Neutron Lifetime // Phys. Rev. Lett. 2013. V. 111. P. 
 222501. arXiv:1309.2623v2 [nucl-ex] 27 Nov 2013.\n\n2. Серебров А
 . П. Разногласие между методом хранения у
 льтрахолодных нейтронов и пучковым мето
 дом при измерении времени жизни нейтрон
 а\, УФН\, т. 189\, № 6\, с. 635–641.\n\n3. Talyshev A. A. On the
  Geometric Approach to Transformations of the Coordinates of Inertial Fram
 es of Reference\, 'Nonlinear Dynamics\, Chaos\, and Complexity'\, Higher E
 ducation Press\, Springer\, 2021\, pp. 113–124.\n
LOCATION:https://researchseminars.org/talk/mmandim/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O. V. Kaptsov
DTSTART:20210916T110000Z
DTEND:20210916T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/24/"
 >Symmetries and solutions of the three-dimensional Kadomtsev — Petviashv
 ili equation</a>\nby O. V. Kaptsov as part of Mathematical models and inte
 gration methods\n\n\nAbstract\nA symmetry group of the three-dimensional K
 adomtsev — Petviashvili equation is calculated. An example of an invaria
 nt solution is given. Exact solutions for the equation under study in the 
 form of double waves are revealed. The resulting solutions are expressed i
 n terms of elementary functions and describe an interaction between a pair
  of solitons. Smooth bounded rational solutions are also constructed.\n
LOCATION:https://researchseminars.org/talk/mmandim/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Tsarev (Siberian Federal University (Krasnoyarsk\, Russia))
DTSTART:20210930T110000Z
DTEND:20210930T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/25/"
 >Integration of algebraic functions\, polynomial approximation\, nonclassi
 cal boundary problems and Poncelet-type theorems</a>\nby Sergey Tsarev (Si
 berian Federal University (Krasnoyarsk\, Russia)) as part of Mathematical 
 models and integration methods\n\n\nAbstract\nIn this review talk we expos
 e remarkably tight relations between the four topics mentioned in the titl
 e. Starting from the paper by N. H. Abel published in 1826 and subsequent 
 results of Chebyshev and Zolotarev we finish at the recent results by Burs
 kii\, Zhedanov\, Malyshev (et al.)  devoted to algorithmic decidability of
  some identities for the values of the Weierstrass P-function\, unexpected
  elementary geometric applications and many\, many more hidden equivalence
 s in seemingly unrelated areas of analysis\, modern computer algebra and g
 eometry.\n \nThis talk will be given in Russian\, the English version was 
 presented on 16-09-2021 at Beijing-Novosibirsk seminar on geometry and mat
 hematical physics ( http://english.math.pku.edu.cn/conferences/244.html ).
  The video and slides of that talk can be found at https://cloud.mail.ru/p
 ublic/S4Pp/wJ5iFcggM\n
LOCATION:https://researchseminars.org/talk/mmandim/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay N. Osipov (Krasnoyarsk Mathematical Center)
DTSTART:20211014T110000Z
DTEND:20211014T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/26/"
 >Simplification of Nested Real Radicals Revisited</a>\nby Nikolay N. Osipo
 v (Krasnoyarsk Mathematical Center) as part of Mathematical models and int
 egration methods\n\n\nAbstract\nThe problem of simplification of nested ra
 dicals over arbitrary number fields was studied by many authors. The case 
 of real radicals over real number fields is somewhat easier to study (at l
 east\, from theoretical point of view). In particular\, an efficient (i.e.
 \, a polynomial-time) algorithm of simplification of at most doubly nested
  real radicals is known. However\, this algorithm does not guarantee compl
 ete simplification for the case of radicals with nesting depth more than t
 wo. In the talk\, we give a detailed presentation of the theory that provi
 des an algorithm which simplifies triply nested reals radicals over the fi
 eld of rationals. Some new examples of triply (or more) nested real radica
 ls that cannot be simplified are also given.\n
LOCATION:https://researchseminars.org/talk/mmandim/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Zakharov
DTSTART:20211020T120000Z
DTEND:20211020T130000Z
DTSTAMP:20260422T225819Z
UID:mmandim/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/27/"
 >Lumps and lump chain solutions of the KP-I equation</a>\nby Dmitry Zakhar
 ov as part of Mathematical models and integration methods\n\n\nAbstract\nT
 he Kadomstev—Petviashvili equation is one of the fundamental equations i
 n the theory of integrable systems. The KP equation comes in two physicall
 y distinct forms: KP-I and KP-II. The KP-I equation has a large family of 
 rational solutions known as lumps. A single lump is a spatially localized 
 soliton\, and lumps can scatter on one another or form bound states. The K
 P-II equation does not have any spatially localized solutions\, but has a 
 rich family of line soliton solutions.\n\nI will discuss two new families 
 of solutions of the KP-I equation\, obtained using the Grammian form of th
 e tau-function. The first is the family of lump chain solutions. A single 
 lump chain consists of a linear arrangement of lumps\, similar to a line s
 oliton of KP-II. More generally\, lump chains can form evolving polygonal 
 arrangements whose structure closely resembles that of the line soliton so
 lutions of KP-II. I will also show how lump chains and line solitons may a
 bsorb\, emit\, and reabsorb individual lumps.\n
LOCATION:https://researchseminars.org/talk/mmandim/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Pavlov (Lebedev Physical Institute RAS\, Moscow)
DTSTART:20211028T110000Z
DTEND:20211028T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/28/"
 >Non-diagonalisable Hydrodynamic Type Systems\, Integrable by Tsarev's Gen
 eralised Hodograph Method</a>\nby Maxim Pavlov (Lebedev Physical Institute
  RAS\, Moscow) as part of Mathematical models and integration methods\n\n\
 nAbstract\nWe present a wide class of non-diagonalizable hydrodynamic type
  systems\, which can be integrated by Tsarev's generalized hodograph metho
 d. This class of hydrodynamic type systems contains Jordan blocks 2x2 only
 . The Haantjes tensor has vanished. This means such 2N component hydrodyna
 mic type systems possess N Riemann invariants and N double eigenvalues onl
 y.\n\nFirst multi-component example was extracted from El's nonlocal kinet
 ic equation\, describing dense soliton gas. All conservation laws and comm
 uting flows were found. A general solution is constructed.\n
LOCATION:https://researchseminars.org/talk/mmandim/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. I. Tribelsky (Faculty of Physics\, M. V. Lomonosov Moscow State
  University)
DTSTART:20211111T110000Z
DTEND:20211111T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/29/"
 >Fall of Quantum Particle to the Center: Exact solution</a>\nby M. I. Trib
 elsky (Faculty of Physics\, M. V. Lomonosov Moscow State University) as pa
 rt of Mathematical models and integration methods\n\n\nAbstract\nA fall of
  a particle to the center of a singular potential is one of a few fundamen
 tal problems of quantum mechanics. Nonetheless\, its solution is not compl
 ete yet. The known results just indicate that if the singularity of the po
 tential is strong enough\, the spectrum of the Schrodinger equation is not
  bounded from below. However\, the wave functions of the problem do not ad
 mit the limiting transition to the ground state. Therefore\, the unbounded
 ness of the spectrum is only a necessary condition. To prove that a quantu
 m particle indeed can fall to the center\, a wave function describing the 
 fall should be obtained explicitly. This is done in the present paper. Spe
 cifically\, an exact solution of the time-dependent Schrodinger equation c
 orresponding to the fall is obtained and analyzed. A law for the collapse 
 of the region of the wave function localization to a single point is obtai
 ned explicitly. It is shown that the known necessary conditions for the pa
 rticle to fall simultaneously are sufficient.\n
LOCATION:https://researchseminars.org/talk/mmandim/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. V. Schmidt
DTSTART:20211125T110000Z
DTEND:20211125T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/30/"
 >Modeling of the far region of a swirling turbulent wake using the Rodi mo
 del</a>\nby A. V. Schmidt as part of Mathematical models and integration m
 ethods\n\n\nAbstract\nThe work is devoted to the construction of a self-si
 milar solution for the far region of a swirling turbulent wake. The algebr
 aic Rodi model is considered\, which is a simplification of differential e
 quations for the transfer of components of the Reynolds stress tensor. A g
 roup-theoretic analysis of the model is carried out. The reduced system wa
 s solved numerically using a modified shooting method. A detailed comparis
 on of the constructed self-similar solution with results obtained by G.G. 
 Chernykh and A.G. Demenkov by direct numerical integration of the model eq
 uations is performed.\n
LOCATION:https://researchseminars.org/talk/mmandim/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Б.И. Сулейманов
DTSTART:20211209T110000Z
DTEND:20211209T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/31/"
 >Интегрируемое уравнение Абеля второго 
 рода\, возникающее при описании асимптот
 ик симметрийного решения уравнения Корт
 евега-де Вриза</a>\nby Б.И. Сулейманов as part of 
 Mathematical models and integration methods\n\nAbstract: TBA\n\nПредс
 тавлено общее решение обыкновенного диф
 ференциального уравнения первого поряд
 ка с рациональной правой частью\, возник
 ающего при построении асимптотик при бо
 льших значениях времени совместных реше
 ний уравнения Кортевега-де Вриза и стаци
 онарной части его высшей неавтономной с
 имметрии\, определяемой  линейной комбин
 ацией первой высшей автономной симметри
 и уравнения Кортевега-де Вриза и его кла
 ссической симметрии Галилея.  По теореме
  о неявной функции данное общее решение 
 локально находится из первого интеграла
 \, явно выписанного в терминах гипергеом
 етрических функций. Частный случай этог
 о общего решения определяет автомодельн
 ые решения уравнений Уизема\, найденные 
 ранее Г.В. Потеминым в 1988 г. (В известных р
 аботах А.В. Гуревича и Л.П. Питаевского на
 чала 70-х годов было установлено\, что дан
 ные решения уравнений Уизема в главном п
 орядке описывают возникновение незатух
 ающих осциллирующих волн в широком ряде 
 задач с малой дисперсией.) Результат ста
 тьи вновь подтверждает эмпирическое пра
 вило: из интегрируемых уравнений в резул
 ьтате различных предельных переходов мо
 гут получаться лишь в том или ином смысл
 е интегрируемые уравнения. Выдвигается 
 общая гипотеза: интегрируемые обыкновен
 ные дифференциальные уравнения\, подобн
 ые рассматриваемому в статье\, должны во
 зникать и при описании асимптотик при бо
 льших временах других симметрийных реше
 ний эволюционных уравнений\, допускающи
 х применение метода обратной задачи.\n
LOCATION:https://researchseminars.org/talk/mmandim/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. V. Meleshko (School of Mathematics\, Institute of Science\, Sur
 anaree University of Technology\, Nakhon Ratchasima\, Thailand)
DTSTART:20211223T110000Z
DTEND:20211223T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/32/"
 >A Method for Finding Reciprocal Transformations</a>\nby S. V. Meleshko (S
 chool of Mathematics\, Institute of Science\, Suranaree University of Tech
 nology\, Nakhon Ratchasima\, Thailand) as part of Mathematical models and 
 integration methods\n\n\nAbstract\nEquivalence transformations play one of
  the important roles in continuum mechanics. These transformations reduce 
 the original equations to simpler forms. One of the classes of nonlocal eq
 uivalence transformations is the class of reciprocal transformations. Desp
 ite the long history of applications of such transformations in continuum 
 mechanics\, there is no method of obtaining them. Recently such a method w
 as proposed. The method uses group analysis approach and it consists of si
 milar steps as for finding equivalence group of transformations. The new m
 ethod provides a systematic tool for finding classes of reciprocal transfo
 rmations (reciprocal equivalence group of transformations). Similar to the
  classical group analysis this approach can be also applied for finding al
 l discrete reciprocal transformations (not only composing a group). For an
  illustration the method is demonstrated by several models applied in hydr
 odynamics. The author is very thankful to Professor Colin Rogers for attra
 cting my attention to reciprocal transformations.\n
LOCATION:https://researchseminars.org/talk/mmandim/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:К.П. Дружков (МГУ)
DTSTART:20220120T110000Z
DTEND:20220120T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/33/"
 >О вариационных принципах для уравнений 
 пограничного слоя</a>\nby К.П. Дружков (МГУ) a
 s part of Mathematical models and integration methods\n\nAbstract: TBA\n\n
 В докладе будут рассмотрены стационарны
 е уравнения пограничного слоя в эйлеров
 ых переменных (при постоянном давлении п
 оступательно движущегося внешнего пото
 ка). Для этой системы уравнений будет дан
 о полное решение обратной задачи вариац
 ионного исчисления: будет показано\, что 
 не существует ни одного функционала дей
 ствие\, такого что:\n1) среди его стационар
 ных точек содержатся все решения данной 
 системы (и\, быть может\, что-нибудь ещё)\,\n
 2) определяемое им соответствие из теоре
 мы Нётер нетривиально.\n
LOCATION:https://researchseminars.org/talk/mmandim/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yury Stepanyants (University of Southern Queensland\, Toowoomba\, 
 Australia)
DTSTART:20220203T110000Z
DTEND:20220203T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/34/"
 >Formation of envelop solitary waves from the localised pulses within the 
 Ostrovsky equation</a>\nby Yury Stepanyants (University of Southern Queens
 land\, Toowoomba\, Australia) as part of Mathematical models and integrati
 on methods\n\n\nAbstract\nWe study the formation of envelope solitons from
  the Korteweg–de Vries (KdV) solitons in the long term evolution within 
 the framework of the Ostrovsky equation. This equation was derived by L.A.
  Ostrovsky in 1978 for the description of weakly nonlinear oceanic waves a
 ffected by the Earth' rotation. Subsequently\, it became clear that this e
 quation is rather universal\; currently\, it is widely used for the descri
 ption of nonlinear waves in various media. This equation is\, apparently\,
  non-integrable and even does not possess steady solitary wave solutions i
 n application to media with negative small-scale dispersion. As has been s
 hown by Grimshaw and Helfrich (2008)\, long-term evolution of initial puls
 es in the form of small-amplitude KdV soliton results in the emergence of 
 envelope solitons which can be described by the nonlinear Schrodinger (NLS
 ) equation. However\, the generalised NLS equation derived by Grimshaw and
  Helfrich (2008) provides the results which are in contradiction with the 
 numerical simulations. The problem was later revisited by Grimshaw and Ste
 panyants (2020) and was shown that the wave packet asymptotically appearin
 g after a long-term evolution of a KdV soliton can be described by the con
 ventional NLS equation. The solution obtained for an envelope soliton agre
 es well with the results of numerical simulations.\n
LOCATION:https://researchseminars.org/talk/mmandim/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:С.М. Чурилов (Институт солнечно-земн
 ой физики СО РАН\, Иркутск)
DTSTART:20220217T110000Z
DTEND:20220217T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/35/"
 >Безотражательное распространение пове
 рхностных волн на мелкой воде в канале п
 еременной ширины и глубины на фоне неодн
 ородного течения</a>\nby С.М. Чурилов (Инсти
 тут солнечно-земной физики СО РАН\, Иркут
 ск) as part of Mathematical models and integration methods\n\n\nAbstract
 \nВ приближении мелкой воды рассмотрена 
 линейная задача о распространении повер
 хностных волн на фоне неоднородного теч
 ения идеальной жидкости в канале с измен
 яющимися вдоль потока шириной $W(x)$ и глуб
 иной $H(x)$ [1\,2]. Найдены три вида соотношен
 ий\, связывающих скорость течения $U(x)$ и с
 корость распространения волн $c(x) = \\sqrt{gH(x
 )}$\, таких\, что при выполнении любого из н
 их волны произвольной формы распростран
 яются без отражения как по течению\, так 
 и против него. В соответствии с этим выде
 лены три класса безотражательных течени
 й и исследованы их свойства. В течениях к
 ласса А скорости течения и волн связаны 
 простым соотношением $c(x)U(x) = \\Pi = \\mathrm{const}
 $\, обеспечивающим распространение волн 
 без отражения на любые расстояния\, т.е. в
 доль всей оси $x$. В течениях классов В и С 
 скорости связаны дифференциальным урав
 нением первого порядка (своим в каждом к
 лассе)\, которое имеет особые точки. Поэт
 ому здесь в общем случае регулярные реше
 ния существуют лишь на ограниченных инт
 ервалах изменения $x$ (луче или конечном и
 нтервале). Для каждого класса найдены ус
 ловия\, при которых есть регулярные реше
 ния на всей оси $x$. Кроме того\, показано\, 
 что можно конструировать и «составные» 
 безотражательные течения класса В. Общи
 й анализ проблемы проиллюстрирован реше
 ниями для конкретных соотношений между 
 глубиной и скоростью течения.\n\nПубликац
 ии\n\n1. Churilov S.M.\, Stepanyants Yu.A. Reflectionless wave propagati
 on on shallow water with variable bathymetry and current. J. Fluid Mech. 9
 31\, A 15\, 2022\; arXiv:2108.12549v2 [physics.flu-dyn]\, 2021.\n\n2. Chur
 ilov S.M.\, Stepanyants Yu.A. Reflectionless wave propagation on shallow w
 ater with variable bathymetry and current. II. arXiv: 2201.00307v1 [physic
 s.flu-dyn]\, 2022.\n
LOCATION:https://researchseminars.org/talk/mmandim/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ю. В. Брежнев
DTSTART:20220303T110000Z
DTEND:20220303T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/36/"
 >Квантовая «ревизия» теоремы Пифагора</a>
 \nby Ю. В. Брежнев as part of Mathematical models and integration
  methods\n\n\nAbstract\nСтранность этого утвержден
 ия только кажущаяся и оно может быть сфо
 рмулировано даже более экстравагантно. 
 Мы даем «единственно правильное» понима
 ние\, которое стоит за реальным смыслом т
 еоремы Пифагора. Хотя речь идет о класси
 ческом математическом утверждении\, его 
 переформулировка мотивирована квантово
 й темой. А именно\, проблемой понимания и 
 вывода знаменитого правила квантовой ве
 роятности - правила Борна\, - которое запи
 сывается через квадрат модуля $|a|^2$. Если 
 кратко\, то «почему квадрат»? Есть прямой
  ответ на этот вопрос\, а появление этих к
 вадратов\, модулей и двоек - комплексной 
 и обычной вещественной - оказываются сов
 ершенно однотипным.\n\nКлючевыми словами 
 к материалу является задача последовате
 льного логического построения исчислен
 ия (calculus) на векторном пространстве. Тогд
 а рассмотрение известных правил паралле
 лограмма\, неравенства треугольника\, по
 нятия углов\, аксиом скалярного произвед
 ения\, нормы\, топологий и т.д. достаточно 
 заменить на задачу построения количеств
 енных величин на векторах. Отсюда будет 
 следовать сначала собственно Пифагоров
 о утверждение и только потом (!) - вышеука
 занные объекты. Теорема\, при этом\, перес
 тает быть теоремой\, превращаясь\, грубо 
 говоря\, в некоторое естественное минима
 листическое определение\; подробности п
 оследуют. Сам квадрат в «теореме» появля
 ется как единственно возможное следстви
 е. Перечисленные выше элементы школьной 
 геометрии становятся\, в свою очередь\, п
 роизводными от Пифагорова квадрата\, с п
 оследующей ревизией первичности поняти
 я длины. С квантовыми (комплексными) анал
 огами - ситуация точно такая же. Более то
 го\, именно количественно-статистическа
 я идеология и природа квантового правил
 а Борна дает подсказку к «новому взгляду
  на» и наиболее убедительные «объяснени
 я к» этой древней греческой теореме.\n
LOCATION:https://researchseminars.org/talk/mmandim/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O.V. Kaptsov
DTSTART:20220317T110000Z
DTEND:20220317T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/37/"
 >Solutions of the Euler equations and stationary structures in an inviscid
  fluid</a>\nby O.V. Kaptsov as part of Mathematical models and integration
  methods\n\n\nAbstract\nThe Euler equations describing two-dimensional ste
 ady flows of an inviscid fluid are studied. These equations are reduced to
  one equation for the stream function and then\, using the Hirota function
 \, solutions of three nonlinear elliptic equations are found. The solution
 s found are interpreted as sources in a rotating fluid\, jets\, chains of 
 sources and sinks\, vortex structures. We propose a new simple method for 
 constructing solutions in the form of rational expressions of elliptic fun
 ctions. It is shown that the flux of fluid across a closed curve is quanti
 zed in the case of the elliptic Sin-Gordon equation.\n
LOCATION:https://researchseminars.org/talk/mmandim/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.P. Tsarev (Siberian Federal University\, Krasnoyarsk)
DTSTART:20220331T110000Z
DTEND:20220331T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/38/"
 >Generalized factorization of second-order linear partial differential ope
 rators and reflectionless wave propagation in shallow water</a>\nby S.P. T
 sarev (Siberian Federal University\, Krasnoyarsk) as part of Mathematical 
 models and integration methods\n\n\nAbstract\nThis talk will be devoted to
  an interpretation of a recent talk by S.M. Churilov and Yu.A. Stepanyants
  (Reflectionless propagation of surface waves in shallow water in a channe
 l of variable width and depth against the background of an inhomogeneous f
 low\, https://researchseminars.org/talk/mmandim/35/) from the point of vie
 w of the theory of generalized factorization of differential operators ([1
 ]).\n\nAs shown in the works of S.M. Churilov\, Yu.A. Stepanyants et al. (
 [2])\, the factorization of a second-order operator with two independent v
 ariables\, which describes the propagation of waves in an inhomogeneous on
 e-dimensional medium\, into a product of first-order operators results in 
 the appearance of a large family of solutions that describe\, from a physi
 cal point of view\, waves that can be considered propagating without refle
 ction from inhomogeneities.\n\nWe will expose briefly the theory of genera
 lized factorization of second-order partial differential operators\, origi
 nating from the works of outstanding mathematicians of the 19th - early 20
 th century P.-S. Laplace\, G. Darboux\, E. Goursat and others and further 
 developed at the end of the 20th century.\n\nThe generalized factorization
  theory allows us to substantially expand the class of reflectionless solu
 tions.\n\nReferences:\n\n[1] E.I. Ganzha\, S.P. Tsarev\, "Classical method
 s of integration of hyperbolic systems and equations of the second order"\
 , 2007\, KSPU (in Russian)\, http://dx.doi.org/10.13140/2.1.4535.8084 The 
 full text is available at the link: https://www.researchgate.net/profile/S
 ergey-Tsarev/publication/235993531_Klassiceskie_metody_integrirovania_gipe
 rboliceskih_sistem_i_uravnenij_vtorogo_poradka/links/0c96051550c72803c2000
 000/Klassiceskie-metody-integrirovania-giperboliceskih-sistem-i-uravnenij-
 vtorogo-poradka.pdf\n\n[2] Churilov\, Semyon M.\, and Yury A. Stepanyants.
  "Reflectionless wave propagation on shallow water with variable bathymetr
 y and current." Journal of Fluid Mechanics 931 (2022).\n
LOCATION:https://researchseminars.org/talk/mmandim/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А.B. Borisov
DTSTART:20220414T110000Z
DTEND:20220414T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/39/"
 >O(3)-model: Integrability. Stationary and Dynamic Magnetic Structures</a>
 \nby А.B. Borisov as part of Mathematical models and integration methods\
 n\n\nAbstract\nA three-dimensional O(3)-model for a unit vector $n(r)$ has
  numerous application\nin the field theory and in the physics of condensed
  matter. We prove that this model\nis integrable under some differential c
 onstraint\, that is\, under certain restrictions for the\ngradients of fie
 lds $Θ(r)$\, $Φ(r)$\,  parametrizing the vector $n(r)$). Under the prese
 nce of the\ndifferential constraint\, the equations of the models are redu
 ced to a one-dimensional sine-\nGordon equation determining the dependence
  of the field $Θ(r)$ on an auxiliary field $a(r)$\nand to a system of two
  equations $(∇S)(∇S) = 0$\, $\\Delta S = 0$ for a complex-valued funct
 ion\n$S(r) = a(r)+i\\cdot Φ(r)$. We show that the solution of this system
  provide all known before exact\nsolutions of models\, namely\, two-dimens
 ional magnetic instantons and three-dimensional\nstructures of hedgehog ty
 pe.\n\nWe show that the found in this way exact solution of the system for
  the field $S(r)$ leads one to exact solution of equations of O(3)–model
  in the form of an arbitrary implicit function of two variables. Two simpl
 e solutions of these equations are discussed: a new magnetic structure tha
 t represents two straight intersecting vortex threads and a "inclusion" ty
 pe structure.\n\nThe integrability of the dynamical equations the O(3)-mod
 el in four-dimensional pseudo-Euclidean space–time was investigated . We
  use a differential substitution to reduce the equations to the one-dimens
 ional sine-Gordon equation and a system of two equations for a complex-val
 ued function $S(r\, t)$ that uniquely determines a vector $n$. We prove th
 at solving the equations for this function amounts to solving a system of 
 four quasilinear equations for auxiliary fields. We obtain their exact sol
 ution in the form of an implicit function of three variables\, which then 
 determines the exact solutions of the dynamical equations with differentia
 l constraints taken into account. As examples\, we describe the dynamics o
 f a plane vortex in D = (2.1)\, a “hedgehog”-type structure\, and new 
 dynamical topological structure.\n\nReferences:\n\n1. А.Б. Борисо
 в. Трехмерные вихри в модели Гейзенберга
 \, ТМФ\, 2021\, том 208\, номер 3\, 471–480 (A.B. Borisov. Th
 ree-Dimensional Vortices in the Heisenberg Model. Theoretical and Mathemat
 ical Physics\, 208(3): 1256–1264 (2021)).\n\n2. А.Б. Борисов. 
 Об интегрируемости 𝑂(3)–модели. Уфимски
 й математический журнал. Том 13. № 2 (2021). С.
  6-10 (А.B. Borisov\, On integrability of O(3)–model\, Ufimsk. Mat. Zh.
 \, 2021\, Volume 13\, Issue 2\, 6–10).\n\n3. А.Б. Борисов. Ди
 намика трехмерных магнитных структур в 
 модели Гейзенберга. ТМФ\, 2022\, том 210\, номе
 р 1\, страницы 115–127 (A.B. Borisov. Dynamics of Three-Dimensi
 onal Magnetic Structures in the Heisenberg Model. Theoretical and Mathemat
 ical Physics\, 210(1): 99–110 (2022)).\n
LOCATION:https://researchseminars.org/talk/mmandim/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Захар Макридин (ИГиЛ\, Новосибирск)
DTSTART:20220428T110000Z
DTEND:20220428T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/40/"
 >Ветвление периодических решений и зако
 ны сохранения нелинейных уравнений теор
 ии волн (по материалам кандидатской дисс
 ертации)</a>\nby Захар Макридин (ИГиЛ\, Новос
 ибирск) as part of Mathematical models and integration methods\n\n\n
 Abstract\nВ настоящей диссертации рассматри
 ваются два типа задач математической те
 ории нелинейных волн. Первый тип связан 
 с построением семейств асимптотических 
 периодических решений системы слабосвя
 занных обыкновенных дифференциальных у
 равнений\, которая получается при перехо
 де к бегущей переменной в модельной сист
 еме зацепленных уравнений Кортевега — д
 е Фриза. В задачах второго типа исследую
 тся способы построения трехмерных закон
 ов сохранения коммутирующих интегрируе
 мых гидродинамических цепочек и их реду
 кций.\n
LOCATION:https://researchseminars.org/talk/mmandim/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:K.R. Helfrich*\, L.A. Ostrovsky **\, Yu.A. Stepanyants*** (* Depar
 tment of Physical Oceanography\, Woods Hole Oceanographic Institution\, Wo
 ods Hole\, MA USA. ** Department of Applied Mathematics\, University of Co
 lorado\, Boulder\, CO\, USA. *** School of Mathematics\, Physics and Compu
 ting\, University of Southern Queensland\, Toowoomba\, QLD\, 4350\, Austra
 lia)
DTSTART:20220512T120000Z
DTEND:20220512T130000Z
DTSTAMP:20260422T225819Z
UID:mmandim/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/41/"
 >Joint Effects of Rotation and Topography on Internal Solitary Waves</a>\n
 by K.R. Helfrich*\, L.A. Ostrovsky **\, Yu.A. Stepanyants*** (* Department
  of Physical Oceanography\, Woods Hole Oceanographic Institution\, Woods H
 ole\, MA USA. ** Department of Applied Mathematics\, University of Colorad
 o\, Boulder\, CO\, USA. *** School of Mathematics\, Physics and Computing\
 , University of Southern Queensland\, Toowoomba\, QLD\, 4350\, Australia) 
 as part of Mathematical models and integration methods\n\n\nAbstract\nWe p
 resent the results of the recent study of dynamics of nonlinear oceanic so
 litary waves under the influence of the combined effects of nonlinearity\,
  Earth’s rotation\, and depth inhomogeneity. Our consideration is based 
 on the extended model of the Korteweg–de Vries (KdV) equation that in ge
 neral accounts for the quadratic and cubic nonlinearity (the Gardner equat
 ion) with the additional terms incorporating the effects of rotation and s
 lowly varying depth. After a brief historical outline\, using the asymptot
 ic (adiabatic) theory\, we describe a complex interplay between these fact
 ors. As an application\, the case of a two-layer fluid with the variable-d
 epth lower layer is considered using the approximate theory\, as well as t
 hrough numerical solutions of the governing equation that includes all the
  above factors under realistic oceanic conditions. In particular\, differe
 nt scenarios of the soliton propagating toward the “internal beach” (e
 .g.\, zero lower-layer depth) are studied in which the terminal damping ca
 n be caused by radiation or disappearing quadratic nonlinearity (when the 
 layers’ depths become equal). We also consider interaction of a soliton 
 with a long wave providing the energy “pump” compensating the radiatio
 n losses due to rotation so that the soliton can exist infinitely. The lim
 itations of the adiabatic approach due to the radiation and other factors 
 are also demonstrated.\n
LOCATION:https://researchseminars.org/talk/mmandim/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А.В. Слюняев (Институт прикладной фи
 зики РАН\, Нижний Новгород)
DTSTART:20220526T110000Z
DTEND:20220526T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/42/"
 >Морские волны-убийцы: проблема\, задачи 
 и решения</a>\nby А.В. Слюняев (Институт прик
 ладной физики РАН\, Нижний Новгород) as part 
 of Mathematical models and integration methods\n\n\nAbstract\nПредла
 гается обзор исследований\, связанных с 
 т.н. морскими волнами-убийцами — неожида
 нно высокими волнами\, по некоторым данн
 ым появляющимися слишком часто\, чем ожи
 дается. Формулируется проблема океаноло
 гии в ее сегодняшнем понимании\, обознач
 аются направления исследований и постав
 ленные перед ними задачи\, обсуждаются у
 же полученные результаты.\n
LOCATION:https://researchseminars.org/talk/mmandim/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Makarenko (Lavrentyev Institute of Hydrodynamics\, Novosib
 irsk\, Russia)
DTSTART:20220929T110000Z
DTEND:20220929T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/43/"
 >Nonlinear stationary internal waves in a weakly stratified fluid</a>\nby 
 Nikolay Makarenko (Lavrentyev Institute of Hydrodynamics\, Novosibirsk\, R
 ussia) as part of Mathematical models and integration methods\n\n\nAbstrac
 t\nWe consider three classes of problems related to the construction and a
 nalysis of asymptotic solutions of the Euler equations for an inviscid inh
 omogeneous fluid.\n\n1. Stationary solutions such as solitary- and periodi
 c waves in a continuously stratified fluid\, and their limiting regimes\n\
 n2. Parametric families of solutions of the 2.5-layer model of nonlinear l
 ong waves and their applications in oceanology\n\n3. Stationary wave struc
 tures and trapped solitary waves over an uneven bottom\n
LOCATION:https://researchseminars.org/talk/mmandim/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Kaptsov (ICM\, Krasnoyarsk\, Russia)
DTSTART:20221013T110000Z
DTEND:20221013T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/44/"
 >Some solutions of the Euler system of an inviscid incompressible fluid</a
 >\nby Oleg Kaptsov (ICM\, Krasnoyarsk\, Russia) as part of Mathematical mo
 dels and integration methods\n\n\nAbstract\nWe consider a system of two-di
 mensional Euler equations describing the motions of an inviscid incompress
 ible fluid. It reduces to one non-linear equation with partial derivatives
  of the third order. A group of point transformations allowed by this equa
 tion is found. Some invariant solutions and solutions not related to invar
 iance are constructed. The solutions found describe vortices\, jet streams
 \, and vortex-like formations.\n
LOCATION:https://researchseminars.org/talk/mmandim/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.B. Borisov\, D.V. Dolgikh
DTSTART:20221027T110000Z
DTEND:20221027T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/45/"
 >Integration of the equations of the Heisenberg model (2D) and the chiral 
 SU(2) models by differential geometry methods</a>\nby A.B. Borisov\, D.V. 
 Dolgikh as part of Mathematical models and integration methods\n\n\nAbstra
 ct\nIn the report\, to integrate the two-dimensional Heisenberg equation a
 nd the three-dimensional chiral SU(2) model\, the differential-geometric m
 ethod of integration is used\, the essence of which is as follows. First\,
  we perform the hodograph transformation\, i.e. change the role of depende
 nt and independent coordinates. Unlike the standard hodograph transformati
 on\, we do not just introduce derivatives of the old coordinates with resp
 ect to new ones\, but define through these derivatives new fields associat
 ed with the components of the metric tensor that appears when the hodograp
 h transformation is performed. Since the original independent coordinates 
 were Euclidean\, the curvature tensor in terms of the introduced metric mu
 st vanish. Ultimately\, we obtain a self-consistent system of equations fo
 r calculating the components of the metric tensor. In this case\, the equa
 tions guaranteeing the curvature tensor to vanish turn out to be the main 
 ones\, and the system of nonlinear equations of the models is their reduct
 ion. The solutions of the constructed equations make it possible to write 
 the solutions of the original models in the form of implicit functions. It
  is important that the differential-geometric method of model integration\
 , based on the embedding of a non-linear partial differential equation in 
 a certain differential relation in Euclidean space\, makes it possible to 
 analyze a wide variety of spatial structures\, the study of which by other
  methods is extremely difficult. The solutions found in the chiral SU(2) m
 odel describe three-dimensional configurations containing\, in particular\
 , spatial vortices\, sources\, non-localized textures\, and structures wit
 h a mapping degree equal to one\, similar to topological solitons. In the 
 Heisenberg model we find a vortex strip (a limited vortex region in a plan
 e). Many of the obtained solutions depend on arbitrary functions.\n
LOCATION:https://researchseminars.org/talk/mmandim/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay  A. Kudryashov (MEPhI\, Moscow)
DTSTART:20221110T110000Z
DTEND:20221110T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/46/"
 >From the Painlevet test to methods for constructing analytical solutions 
 of nonlinear ODEs</a>\nby Nikolay  A. Kudryashov (MEPhI\, Moscow) as part 
 of Mathematical models and integration methods\n\n\nAbstract\nThe applicat
 ion of the Painlevet test to analyze nonlinear ordinary differential equat
 ions is discussed. A brief review of classical works by S. V. Kovalevskaya
  on solving the problem of motion of a rigid body with a fixed point and w
 orks by P. Penleve on the classification of one class of second-order equa
 tions is given. The well-known example of the Korteweg–de Vries equation
  taking into account the traveling wave solutions illustrates the Painleve
 t property for a nonlinear oscillator. Special attention is paid to non-in
 tegrable partial differential equations such as the Korteweg–de Vries–
 Burgers equation and the Kuramoto–Sivashinsky equation. Using traveling 
 wave solutions\, the construction of analytical solutions to these equatio
 ns is illustrated. Possible applications of the simplest equations method 
 for constructing analytical solutions of non-integrable differential equat
 ions are discussed. The application of the method for constructing optical
  solitons of a generalized nonlinear Schrodinger equation of unrestricted 
  order with nonlinearity in the form of a polynomial is illustrated.\n
LOCATION:https://researchseminars.org/talk/mmandim/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.M. Churilov (Institute of Solar-Terrestrial Physics\, Irkutsk)
DTSTART:20221124T110000Z
DTEND:20221124T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/47/"
 >On the stability of sharply stratified shear flows with inflection-free v
 elocity profiles</a>\nby S.M. Churilov (Institute of Solar-Terrestrial Phy
 sics\, Irkutsk) as part of Mathematical models and integration methods\n\n
 \nAbstract\nWe study the linear stability of shear flows with sharp strati
 fication ($l \\ll L$\, where $l$ and $L = 1$ are vertical scales of densit
 y and velocity variation respectively) and a monotonic velocity profile $V
 _x = U(z)$ which has no inflection points and increases from $U = 0$ at th
 e bottom ($z = 0$) to $U = 1$ when $z \\to +\\infty$\, $U'(0) = 1$. We sho
 w that such a flow with step density variation ($l = 0$) and $U'' < 0$ has
  the instability domain of an universal form on the ($k$\, $J$) plane\, wh
 ere $k$ is the wave number and $J$ is the bulk Richardson number. Namely\,
  the\ndomain is bounded by abscissa axis ($J = 0$)\, dispersion curve $J =
  J(k\, c = 1)\,$ and\nthe segment of ordinate axis ($k = 0$) connecting th
 em. Here $c$ is the phase velocity\nof the wave. The role of null-curvatur
 e points on the velocity profile (where\n$U'' = 0$\, but does not change i
 ts sign) in the transformation of such an instability\ndomain into that of
  a flow with a piecewise linear velocity profile is discussed.\n\nIt is sh
 own that in continuously stratified flows with $0 < l \\ll 1$\, a countabl
 e\ninfinity of oscillation modes appears with $J = J_m(k\,c)$\, $m = 0\,1\
 ,2\,\\ldots$. For any $m$\,\nstreamwise propagating (i.e.\, $y$-independen
 t) waves have instability domain\nextending from the upper boundary\,\n\n$
 J = J_0^{(+)}(k) = J_0(k\,c=1) = O(1)$ or $J = J_m^{(+)}(k) = J_m(k\,c=1) 
 = O(m^2l^{-1})$\, $m \\ge 1$\nto the lower one\,\n\n$J = J_0^{(-)}(k) > 0$
 \, where $J_0^{(-)}(k) = O(l^2)$ when $l < k < 1$\, or\n\n$J = J_m^{(-)}(k
 ) > 0$\, where $J_m^{(-)}(k) = O(m^2l)$ when $l^{3/2} < k < l^{1/2}$\, $m 
 \\ge 1$.\n\nBy virtue of Squire's theorem\, the lower "stability bands" (b
 etween $J_m^{(-)}(k)$ and the\n$J = 0$ axis) are filled with unstable obli
 que waves. When $J$ is in the range from\n$O(l^2)$ to $O(l)$\, unstable ob
 lique and streamwise propagating waves (mainly\nbelonging to $m = 0$ mode)
  successfully compete\, and a wide spectrum of three-\ndimensional unstabl
 e waves with close streamwise phase velocities and\ncomparable growth rate
 s is excited.\n
LOCATION:https://researchseminars.org/talk/mmandim/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. D. Yunakovsky
DTSTART:20221208T110000Z
DTEND:20221208T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/48/"
 >Methods for numerical simulation of NLS</a>\nby A. D. Yunakovsky as part 
 of Mathematical models and integration methods\n\n\nAbstract\nThe advent o
 f supercomputers made it possible to model multidimensional NLS and reveal
 ed new problems: new parallelizable algorithms were required.\n\nFor equat
 ions of the "parabolic" type\, which include the non-stationary Schröding
 er equation\, numerical schemes have very stringent stability conditions: 
 $\\Delta t < \\Delta x^2$\, which\, in fact\, slows down the solution of t
 he problem when the grid is refined. In addition\, in equations of the NLS
 E type\, high spatial harmonics do not decay with time\, but have rapidly 
 changing phases\, which leads even under a "relatively mild" condition of 
 stability to the phenomenon of random phases.\n\nA review of grid and spec
 tral methods for finding approximate solutions of the NSE is given\, and t
 he possibilities of using the FFT are analyzed. The problem of increasing 
 the counting step with respect to time and typical errors are discussed. B
 rief reviews of the use of the operator exponential method and the method 
 of nonreflecting boundary conditions are given. The possibilities of the h
 yperbolization method for NLS are discussed.\n
LOCATION:https://researchseminars.org/talk/mmandim/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. P. Tsarev (Siberian Federal University\, Krasnoyarsk)
DTSTART:20221222T110000Z
DTEND:20221222T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/49/"
 >The Monge problem: From quadrature-free integration of underdetermined no
 nlinear ODEs to efficient car parking</a>\nby S. P. Tsarev (Siberian Feder
 al University\, Krasnoyarsk) as part of Mathematical models and integratio
 n methods\n\n\nAbstract\nThis talk is about an old topic of finding closed
 -form solutions of UNDERDETERMINED systems of nonlinear ordinary different
 ial equations\, started by G.Monge in 1784 and later followed by Goursat (
 1905)\, Hilbert (1913) and Cartan (1914).\n\nIn the last decades of the XX
  century these problems draw attention of specialists in nonlinear control
 . In particular\, the technique of this problem was used in developing mot
 ion algorithms for nonholonomic mechanical systems\, a typical example bei
 ng a car with N trailers. Parking such a "car train" moving back is a popu
 lar difficult task! Modern results based on the old investigations of Gour
 sat make automatic control of such vehicles possible.\n\nFor those interes
 ted in the problem of integration of ODEs and PDEs: using the results desc
 ribed one can often remove (unnecessary) quadratures in the final expressi
 ons for the complete solution of a C-integrable nonlinear PDEs.\n\nWe expo
 se the classical results by Cartan and Hilbert showing the intruiging deta
 ils of the Monge problem.\n
LOCATION:https://researchseminars.org/talk/mmandim/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.M.Churilov\, I.G. Shukhman (Institute of Solar-Terrestrial Physi
 cs\, Irkutsk)
DTSTART:20230126T110000Z
DTEND:20230126T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/50/"
 >Critical layer and weakly nonlinear evolution of unstable quasi-monochrom
 atic perturbations in shear flows</a>\nby S.M.Churilov\, I.G. Shukhman (In
 stitute of Solar-Terrestrial Physics\, Irkutsk) as part of Mathematical mo
 dels and integration methods\n\n\nAbstract\nBy Howard’s semicircle theor
 em\, in a plane-parallel shear flow\, the real part of the phase velocity 
 $c$ of an unstable perturbation $\\sim f(z)\\exp[ik(x-ct)]$ is between the
  minimum and maximum of the flow velocity $V_x = U(z)$ and coincides with 
 $U$ on a critical level $z=z_c$ so that $\\mathrm{Re} \\\, c = U(z_c)$. In
  a narrow neighborhood of this level\, — so called critical layer (CL)\,
  — liquid particles are in phase resonance with the wave and intensively
  interact with it. In the framework of an idealized statement of the probl
 em taking no account of dissipation (viscosity)\, unsteadiness\, and nonli
 nearity\, the perturbation eigenfunction $f(z)$ is singular on the critica
 l level. Taking into consideration any one of these factors makes the solu
 tion regular\, but the relative magnitude of the perturbation inside the C
 L remains large. For this reason\, it is the CL that makes the leading-ord
 er contribution into nonlinear interactions\, and this fact simplifies the
  study of a weakly nonlinear evolution of an unstable perturbation.\n\nEac
 h of these factors specifies the length scale associated with it\, namely\
 ,\n\n(i) viscous $L_ν = (k^3 \\mathrm{Re})^{-1/3} = O(ν^{1/3})$\,\n\n(ii
 ) unsteady $L_t = |(kU'_c A)^{-1} d|A|/dt| = O(γ)$\,\n\n(iii) nonlinear $
 L_N \\sim |A/U'_c|^δ$\,\n\nwhere $\\mathrm{Re}$ is Reynolds number\, $A(t
 )$ is the perturbation amplitude\, $δ$ depends on the behavior of $f(z)$ 
 in the neighborhood of the critical level\, and the prime denotes the deri
 vative in $z$. The greatest of these scales determines not only the width 
 of the CL\, but also the behavior of the solution inside it. Therefore\, i
 t is appropriate to distinguish between viscous\, unsteady\, and nonlinear
  CLs\, taking into account that the CL kind may change in the process of e
 volution in accordance with the scale ratio.\n\nAs a result\, only a limit
 ed number of basic scenarios of evolution do exist. The realization of one
  scenario or another\, or some sequence of them depends mainly on the degr
 ee of supercriticality of the basic unstable flow and on the nature of the
  singularity at the critical level.\n
LOCATION:https://researchseminars.org/talk/mmandim/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А. В. Боровских (МГУ)
DTSTART:20230209T110000Z
DTEND:20230209T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/51
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/51/"
 >Групповой анализ уравнения эйконала</a>\n
 by А. В. Боровских (МГУ) as part of Mathematical models and 
 integration methods\n\n\nAbstract\nВ докладе будут предс
 тавлены результаты группового анализа у
 равнения эйконала — уравнения\, описыва
 ющего фронт распространяющейся волны. А
 ктуальность такого анализа возникла в с
 вязи с исследованием распространения во
 лн в неоднородной и анизотропной среде. 
 В волновой теории обычно предполагается
 \, что эйконал уже известен\, а на самом де
 ле для каких сред (кроме канонической од
 нородной) уравнение эйконала можно прои
 нтегрировать — было неизвестно.\n\nГрупп
 овая классификация сначала трехмерных\, 
 затем двумерных\, а в конце концов — аниз
 отропных уравнений показала\, что задача
  групповой классификации оказывается на
 иболее содержательной и продуктивной то
 лько в наиболее общей постановке. Именно
  тогда обнаруживаются четкие связи с гео
 метрией\, физикой и аналитическими свойс
 твами уравнений. Именно поэтому получен
 ная классификация\, вместе со всей совок
 упностью указанных связей\, может рассма
 триваться как образцовая.\n
LOCATION:https://researchseminars.org/talk/mmandim/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.M.Churilov (Institute of Solar-Terrestrial Physics\, Irkutsk)
DTSTART:20230302T110000Z
DTEND:20230302T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/52/"
 >Weakly-nonlinear stage of instability development in shear flows with an 
 inflection-free velocity profile and thin pycnocline</a>\nby S.M.Churilov 
 (Institute of Solar-Terrestrial Physics\, Irkutsk) as part of Mathematical
  models and integration methods\n\n\nAbstract\nWeakly stratified flows of 
 the class under study have a wide 3D spectrum of unstable waves with very 
 close growth rates. What is more\, their phase velocities differ little an
 d therefore their individual critical layers merge into a common one. On t
 his basis\, nonlinear evolution equations describing the perturbation deve
 lopment are derived and analyzed. Their solutions demonstrate that\, throu
 ghout a weakly nonlinear stage of development\, wave amplitudes grow explo
 sively. During the first (three-wave) phase\, the most rapidly growing are
  low-frequency waves whereas at the next phase\, when numerous and diverse
  higher-order wave interactions come into play\, the growth of high-freque
 ncy waves is accelerated and they overtake low-frequency waves. The result
 s obtained are illustrated by numerical calculations for some ensembles of
  waves.\n
LOCATION:https://researchseminars.org/talk/mmandim/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:E.A. Kuznetsov (P.N. Lebedev Physical Institute of RAS\, Moscow\, 
 Russia)
DTSTART:20230316T110000Z
DTEND:20230316T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/53/"
 >Folding in fluids</a>\nby E.A. Kuznetsov (P.N. Lebedev Physical Institute
  of RAS\, Moscow\, Russia) as part of Mathematical models and integration 
 methods\n\n\nAbstract\nThe formation of the coherent vortical structures i
 n the form of thin pancakes for three-dimensional flows is studied at the 
 high Reynolds regime when\, in the leading order\, the development of such
  structures can be  described within the Euler equations for ideal incompr
 essible fluids. Numerically and analytically on the base of the vortex lin
 e representation [1\, 2] we show that compression of such structures and r
 espectively increase of their amplitudes are possible due to the compressi
 bility of the vorticity in the 3D case [3]. It is demonstrated that this g
 rowth has an exponential behavior and can be considered as folding (analog
  of breaking) for the divergence-free fields of vorticity. At high amplitu
 des this process in 3D has a self-similar behavior connected the maximal v
 orticity and the pancake width by the relation of the universal type [4].\
 n\n[1] E.A. Kuznetsov\, V.P. Ruban\, Hamiltonian dynamics of vortex lines 
 for systems of the hydrodynamic type\, Pis’ma ZhETF \, 76\, 1015 (1998) 
 [JETP Letters\, 67\, 1076-1081 (1998)].\n\n[2] E.A. Kuznetsov\, Vortex lin
 e representation for flows of ideal and viscous fluids \, Pis’ma v ZHETF
 \, 76\, 406-410 (2002) [JETP Letters\, 76\, 346-350 (2002)].\n\n[3] D.S. A
 gafontsev\, E.A. Kuznetsov\, A.A. Mailybaev\, and E.V. Sereshchenko\, Comp
 ressible vortex structures and their role in the hydrodynamical turbulence
  onset\, UFN 192\, 205-225 (2022) [Physics Uspekhi\, 65 189 - 208 (2022)].
 \n\n[4] D.S. Agafontsev\, E.A. Kuznetsov and A.A. Mailybaev\, Development 
 of high vorticity structures and geometrical properties of the vortex line
  representation\, Phys. Fluids 30\, 095104-13 (2018)\; Stability of tangen
 tial discontinuity for the vortex pancakes\, Pisma ZHETF\, 114\, 67-71 (20
 21) [JETP Letters\, 2021\, 114\, 71–75 (2021)].\n
LOCATION:https://researchseminars.org/talk/mmandim/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Y. Stepanyants (University of Southern Queensland)
DTSTART:20230330T110000Z
DTEND:20230330T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/54
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/54/"
 >Solitary waves in the cylindrical Kadomtsev–Petviashvili equation</a>\n
 by Y. Stepanyants (University of Southern Queensland) as part of Mathemati
 cal models and integration methods\n\n\nAbstract\nWe present exact solutio
 ns in the form of solitary waves in the cylindrical Kadomtsev–Petviashvi
 li (cKP) equation (alias Johnson equation) which describes nonlinear wave 
 processes in dispersive media. This equation belongs to the class of compl
 etely integrable systems\; however\, its exact solutions were not studied 
 in detail albeit some particular solutions were found. We show that this e
 quation has relationships with the classical Korteweg–de Vries and plane
  Kadomtsev–Petviashvili equations. Using these relationships\, some new 
 solutions can be formally obtained that represent cylindrically diverging 
 solitary waves and compact solitary waves called lumps. We demonstrate int
 eresting properties of lumps solutions specific for the cylindrical geomet
 ry. Exact solutions describing normal and anomalous lump interactions are 
 found and graphically illustrated.\n
LOCATION:https://researchseminars.org/talk/mmandim/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:М.В. Павлов (ФИАН\, Москва)
DTSTART:20230413T110000Z
DTEND:20230413T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/55
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/55/"
 >Эллиптические ортогональные системы ко
 ординат и разделение переменных в опера
 торе Лапласа</a>\nby М.В. Павлов (ФИАН\, Москв
 а) as part of Mathematical models and integration methods\n\n\nAbstract\n
 Разделение переменных в системах уравне
 ний в частных производных — одна из важн
 ых и интересных задач. Прекрасный обзор 
 этой области был представлен в книге Э. Т
 . Уиттекера и Дж. Н. Ватсона в 1905 году.\n\nВ 
 докладе будет предложена интерпретация 
 известных результатов\, которая позволи
 т лучше понять препятствия и возможност
 и в теории разделения независимых перем
 енных.\n
LOCATION:https://researchseminars.org/talk/mmandim/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:K.R. Khusnutdinova (Department of Mathematical Sciences\, Loughbor
 ough University\, UK)
DTSTART:20230427T110000Z
DTEND:20230427T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/56
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/56/"
 >On elliptic cylindrical Kadomtsev-Petviashvili equation for surface waves
 </a>\nby K.R. Khusnutdinova (Department of Mathematical Sciences\, Loughbo
 rough University\, UK) as part of Mathematical models and integration meth
 ods\n\n\nAbstract\nThere exist two classical versions of the Kadomtsev-Pet
 viashvili (KP) equation [1]\, related to the Cartesian and cylindrical geo
 metries of the waves (derivations for surface waves were given in [2] and 
 [3]\, respectively). We derived and studied a version related to the ellip
 tic-cylindrical geometry in [4] (joint work with Klein\, Matveev and Smirn
 ov). The derivation was given from the full set of Euler equations for sur
 face gravity waves with the account of surface tension. The ecKP equation 
 contains a parameter\, and it reduces to the cKP equation both when this p
 arameter tends to zero\, and when the solutions are considered at distance
 s much larger than that parameter. We showed that there exist transformati
 ons between all three versions of the KP equation associated with the phys
 ical problem formulation (KP\, cKP and ecKP equations)\, and used them to 
 obtain new classes of approximate solutions for the Euler equations. The s
 olutions exist on the whole plane (at least formally).  We hope that they 
 could be useful in describing an intermediate asymptotics for the problems
  where sources\, boundaries and obstacles have elliptic or nearly-elliptic
  geometry.\n\nReferences:\n\n[1] B.P. Kadomtsev\, V.I. Petviashvili\, On t
 he stability of solitary waves in weakly dispersing media\, Sov. Phys. Dok
 l.\, 15 (1970) 539-541.\n\n[2] M.J. Ablowitz and H. Segur\, On the evoluti
 on of packets of water waves\, J. Fluid Mech.\, 92 (1979) 691-715.\n\n[3] 
 R.S. Johnson\, Water waves and Korteweg - de Vries equations\, J. Fluid Me
 ch.\, 97 (1980) 701-719.\n\n[4] K.R. Khusnutdinova\, C. Klein\, V.B. Matve
 ev\, A.O. Smirnov\, On the integrable elliptic cylindrical Kadomtsev-Petvi
 ashvili equation\, Chaos 23 (2013) 013126.\n
LOCATION:https://researchseminars.org/talk/mmandim/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Б.И. Сулейманов (Институт математики
  с вычислительным центром УФИЦ РАН\, Уфа)
DTSTART:20230511T110000Z
DTEND:20230511T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/57/"
 >Мероморфность решений широкого класса 
 обыкновенных дифференциальных уравнени
 й типа Пенлеве</a>\nby Б.И. Сулейманов (Инсти
 тут математики с вычислительным центром
  УФИЦ РАН\, Уфа) as part of Mathematical models and integration 
 methods\n\n\nAbstract\nДоклад основан на двух совм
 естных с А.В. Домриным и М.А. Шумкиным пуб
 ликациях.\n\n1. Домрин А. В.\, Сулейманов Б.И.
 \, Шумкин М. А. О глобальной мероморфности
  решений уравнений Пенлеве и их иерархий
 . Анализ и математическая физика\, Сборни
 к статей. К 70-летию со дня рождения профе
 ссора Армена Глебовича Сергеева\, Тр. МИА
 Н\, 311\, МИАН\, М.\, 2020\, 106–122 (A. V. Domrin\, \, B. I. Sule
 imanov \, and M. A. Shumkin. Global Meromorphy of Solutions of the Painlev
 é Equations and Their Hierarchies. Proceedings of the Steklov Institute o
 f Mathematics\, 2020\, Vol. 311\, Issue 1\, pp. 98–113).\n\n2. V. Domrin
 \, M. A. Shumkin and B. I. Suleimanov. Meromorphy of solutions for a wide 
 class of ordinary differential equations of Painlevé type. Journal of Mat
 hematical Physics. Vol.: 63. Issue 2 (2022).\n\nОтталкиваясь 
 от на результатов  А.В. Домрина о локальн
 ой по времени мероморфной продолжимости
  из области аналитчности решений солито
 нных уравнений параболического типа\, в  
 докладе будет доказана мероморфность ре
 шений начальных задач для широкого клас
 са обыкновенных дифференциальных уравн
 ений.  Эти обыкновенные дифференциальны
 е уравнения задаются инвариантными мног
 ообразиями нелинейных уравнений в частн
 ых производных параболического типа\, ин
 тегрируемых методом обратной задачи рас
 сеяния. В качестве примеров рассмотрены 
 случаи некоторых из уравнений Пенлеве и 
 их иерархий.\n
LOCATION:https://researchseminars.org/talk/mmandim/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:E. I. Kaptsov (Suranaree University of Technology\, Thailand)
DTSTART:20230525T110000Z
DTEND:20230525T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/58/"
 >Methods for constructing invariant conservative finite-difference schemes
  for hydrodynamic-type equations</a>\nby E. I. Kaptsov (Suranaree Universi
 ty of Technology\, Thailand) as part of Mathematical models and integratio
 n methods\n\n\nAbstract\nWhen choosing suitable finite-difference schemes 
 for equations of hydrodynamic type\, preference is given to various proper
 ties of schemes\, such as their monotonicity\, stability\, conservation of
  phase volumes\, etc. In the present report\, we focus on the criterion of
  invariance of schemes\, i.e. we consider finite-difference equations and 
 meshes that preserve the symmetries of the original differential equations
 .\n\nFor equations of the hydrodynamic type\, the construction of invarian
 t difference schemes is often significantly simplified if the equations ar
 e considered in Lagrange coordinates. In this case\, uniform orthogonal me
 shes can be used\, which retain their geometric structure under the action
  of group transformations inherited from the original equations. In additi
 on\, in Lagrangian  coordinates\, it is easier to find conservation laws b
 oth for differential equations and for the corresponding invariant differe
 nce schemes. In a number of cases\, it is possible to construct invariant 
 conservative schemes that possess difference analogues of all local conser
 vation laws of the original models.\n\nThe report is primarily devoted to 
 the practical aspects of designing schemes of the described type. For this
 \, a number of special techniques and methods have been developed. The mos
 t convenient is the finite-difference analogue of the direct method\, as w
 ell as the technique of constructing schemes based on approximations of co
 nservation laws.\nVarious equations of the theory of shallow water and one
 -dimensional equations of magnetohydrodynamics are considered as examples.
 \n\nReferences\n\n1. Dorodnitsyn V. A.\, Kaptsov E. I.\, Discrete shallow 
 water equations preserving symmetries and conservation laws. J. Math. Phys
 .\, 62(8):083508\, 2021.\n\n2. Kaptsov E. I.\, Dorodnitsyn V. A.\, Meleshk
 o S. V.\, Conservative invariant finite-difference schemes for the modifie
 d shallow water equations in Lagrangian coordinates. Stud. Appl. Math.\, 2
 022\; 149: 729–761.\n\n3. Dorodnitsyn V. A.\, Kaptsov E. I.\, and Melesh
 ko S. V.\, Symmetries\, conservation laws\, invariant solutions and differ
 ence schemes of the one-dimensional Green–Naghdi equations. J. Nonlinear
  Math. Phys.\, 28:90–107\, 2020.\n\n4. Cheviakov A. F.\, Dorodnitsyn V. 
 A.\, Kaptsov E. I.\, Invariant conservation law-preserving discretizations
  of linear and nonlinear wave equations\, J. Math. Phys.\, 61 (2020) P. 08
 1504.\n\n5. Dorodnitsyn V. A.\, Kaptsov E. I.\, Invariant finite-differenc
 e schemes for plane one-dimensional MHD flows that preserve conservation l
 aws. Mathematics\, 10(8):1250\, 2022.\n\n6. Kaptsov E. I.\, Dorodnitsyn V.
  A.\, Invariant conservative finite-difference schemes for the one-dimensi
 onal shallow water magnetohydrodynamics equations in Lagrangian coordinate
 s. Submitted. Preprint: <a href=https://arxiv.org/abs/2304.03488>https://a
 rxiv.org/abs/2304.03488</a>.\n\n7. Kaptsov E. I.\, Dorodnitsyn V. A.\, Mel
 eshko S. V.\, Invariant finite-difference schemes for cylindrical one-dime
 nsional MHD flows with conservation laws preservation. Submitted. Preprint
 : <a href=http://dx.doi.org/10.48550/arXiv.2302.05280>http://dx.doi.org/10
 .48550/arXiv.2302.05280</a>.\n
LOCATION:https://researchseminars.org/talk/mmandim/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:К. Дружков (Российско-Армянский унив
 ерситет\, Ереван)
DTSTART:20230921T110000Z
DTEND:20230921T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/59
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/59/"
 >Внутренние лагранжианы как вариационны
 е принципы</a>\nby К. Дружков (Российско-Арм
 янский университет\, Ереван) as part of Mathematica
 l models and integration methods\n\n\nAbstract\nКлассический 
 принцип стационарного действия связан с
  лагранжианами\, определёнными на простр
 анствах джетов. Соответствующие уравнен
 ия движения представляют собой поверхно
 сти в таких пространствах. Оказывается\, 
 что в дополнение к этому принцип стацион
 арного действия всегда воспроизводит се
 бя на уровне внутренней геометрии соотв
 етствующего вариационного уравнения. Пр
 и этом возникает «внутренний интегральн
 ый функционал»\, определённый на классе 
 особых подмногообразий уравнения. Эти п
 одмногообразия имеют размерность как у 
 решений и склеены из начально-краевых ус
 ловий\, продолженных на старшие производ
 ные\; в этом смысле они представляют собо
 й «почти решения».\n\nВсе решения вариаци
 онных уравнений заведомо являются стаци
 онарными точками внутренних интегральн
 ых функционалов в соответствующих класс
 ах почти решений. В зависимости от ситуа
 ции стационарными точками таких функцио
 налов могут быть не только решения. Одна
 ко если почти решение уравнений Эйлера 
 — Лагранжа склеено из нехарактеристиче
 ских начально-краевых условий\, оно явля
 ется стационарной точкой соответствующ
 его внутреннего функционала тогда и тол
 ько тогда\, когда оно является решением.\n
 \nВ этой связи удаётся также сформулиров
 ать соответствующую версию теоремы Нёте
 р\, согласно которой всякая симметрия ва
 риационных уравнений либо определяет за
 коны сохранения\, либо порождает внутрен
 ние интегральные функционалы.\n\nПредлаг
 аемая конструкция служит ответом на воп
 рос о том\, почему внутренняя геометрия в
 ариационных уравнений знает об их вариа
 ционной природе: функционал действие вс
 егда воспроизводит себя внутри соответс
 твующих уравнений с помощью порождаемог
 о им внутреннего функционала.\n
LOCATION:https://researchseminars.org/talk/mmandim/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Kaptsov (ICM SB RAS\, Krasnoyark\, Russia)
DTSTART:20231005T110000Z
DTEND:20231005T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/60/"
 >Solutions of some wave models of mechanics</a>\nby Oleg Kaptsov (ICM SB R
 AS\, Krasnoyark\, Russia) as part of Mathematical models and integration m
 ethods\n\n\nAbstract\nThe paper deals with one-dimensional nonstationary s
 econd order partial derivative equations describing waves in inhomogeneous
  and nonlinear media.\n\nContact transformations and differential Euler su
 bstitutions are used to construct solutions.\n\nGeneral solutions of some 
 nonstationary models of continuum mechanics are found.\n
LOCATION:https://researchseminars.org/talk/mmandim/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.V. Borovskikh\, K.S. Platonova (MSU\, Moscow\, Russia)
DTSTART:20231019T110000Z
DTEND:20231019T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/61/"
 >Group analysis of the one-dimentional kinetic equation and the problem of
  closing the moment system</a>\nby A.V. Borovskikh\, K.S. Platonova (MSU\,
  Moscow\, Russia) as part of Mathematical models and integration methods\n
 \n\nAbstract\nThe report is devoted to a problem that goes back to the wor
 ks of Maxwell and Clausius\, the relationship between the kinetic equation
 s of the particles of the medium and the macroscopic characteristics of th
 e medium. In the modern form\, the question is how to obtain the equations
  of a continuum media from the kinetic equations. The fundamental problem 
 is the following: integration of the kinetic equation with power-law weigh
 ts over velocities gives an infinite system of equations\, the first of wh
 ich are very similar to the equations of a continuous medium. But the syst
 em of equations of a continuous medium is finite. This means that the infi
 nite system must be truncated and closed. The problem consists of two ques
 tions: where to truncate and what ratio use to close. The report will pres
 ent an approach based on group methods. The idea is to calculate the symme
 try group of the kinetic equation\, transfer its action to macroscopic qua
 ntities\, find invariants already in terms of macroscopic quantities\, and
  use them to construct a closure. This was successfully implemented in the
  one-dimensional case\, the details will be presented in the report.\n
LOCATION:https://researchseminars.org/talk/mmandim/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.L. Mironov\, S.V. Mironov (Institute for physics of microstructu
 res RAS\, Nizhny Novgorod\, Russia)
DTSTART:20231102T110000Z
DTEND:20231102T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/62
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/62/"
 >Sedeonic generalization of hydrodynamic equations. Vortex  models of plan
 e turbulent walls-bounded flows</a>\nby V.L. Mironov\, S.V. Mironov (Insti
 tute for physics of microstructures RAS\, Nizhny Novgorod\, Russia) as par
 t of Mathematical models and integration methods\n\n\nAbstract\nWe discuss
  a generalization of hydrodynamic equations based on the anticommutative s
 pacetime\nalgebra of 16-component sedeons. A symmetric system of Maxwell-t
 ype equations is\nobtained\, which describes the longitudinal motion and r
 otation of vortex tubes. Based on these\nequations\, a simple model of a p
 lane\, fully developed turbulent flow is proposed. As examples\,\nwe consi
 der turbulent near-wall flows\, as well as Couette and Poiseuille flows in
  rectangular\nchannels.\n
LOCATION:https://researchseminars.org/talk/mmandim/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.V. Shmidt (Institute of computational modelling SB RAS\, Krasnoy
 arsk\, Russia)
DTSTART:20231116T110000Z
DTEND:20231116T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/63/"
 >Approximate solution to a model of the far momentumless turbulent wake</a
 >\nby A.V. Shmidt (Institute of computational modelling SB RAS\, Krasnoyar
 sk\, Russia) as part of Mathematical models and integration methods\n\n\nA
 bstract\nThe flow in the far momentumless turbulent wake is described with
  the use of a mathematical model based on the Rodi’s algebraic model of 
 Reynolds stresses. Similarity reduction of the model to a system of ordina
 ry differential equations is obtained. Asymptotic expansion of a solution 
 in the vicinity of a singular point is used to construct approximate solut
 ion of the corresponding boundary value problem.\n
LOCATION:https://researchseminars.org/talk/mmandim/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phil Broadbridge (La Trobe University\, Australia and IMI-Kyushu U
 niversity\, Japan)
DTSTART:20231130T110000Z
DTEND:20231130T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/64/"
 >Reaction-diffusion models for fish populations with realistic mobility</a
 >\nby Phil Broadbridge (La Trobe University\, Australia and IMI-Kyushu Uni
 versity\, Japan) as part of Mathematical models and integration methods\n\
 n\nAbstract\nNonlinear reaction-diffusion equations\, with Fisher logistic
  growth and constant diffusion coefficient\, have been used in fisheries r
 esearch to estimate sustainable harvesting rates and critical domain sizes
  of no-take areas. However\, constant diffusivity in a population density 
 corresponds to standard Brownian motion of individuals\, with a normal dis
 tribution for displacement over a fixed time interval. For available good 
 data sets on mobile fish populations\, the distribution is certainly not n
 ormal. The data can be fitted with a long-tailed Lévy distribution that c
 orresponds to diffusion by fractional Laplacian.\n\nWe have developed exac
 t solutions for realistic Fisher-Kolmogorov-Petrovski-Piscounov  models wi
 th diffusion by fractional Laplacian. These can also account for a delay i
 n the reaction term. It is then shown how to modify critical domain sizes 
 of protected areas.\n
LOCATION:https://researchseminars.org/talk/mmandim/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ranis Ibragimov (Mathematics & Computer Science\, De Gruyter\, Bos
 ton\, MA\, USA)
DTSTART:20231214T123000Z
DTEND:20231214T133000Z
DTSTAMP:20260422T225819Z
UID:mmandim/65
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/65/"
 >Invariant Solutions of Nonlinear Mathematical Modeling of Natural Phenome
 na</a>\nby Ranis Ibragimov (Mathematics & Computer Science\, De Gruyter\, 
 Boston\, MA\, USA) as part of Mathematical models and integration methods\
 n\n\nAbstract\nThe main objective is to demonstrate the advantages of the 
 invariance method in obtaining new exact analytic solutions expressed in t
 erms of elementary functions for various physical phenomena. As one partic
 ular application of the invariance method will be the mathematical modelin
 g of oceanic and atmospheric whirlpools causing weather instabilities and\
 , possibly\, linked with climate change. As another particular example\, i
 t will be demonstrated that the invariance method allows to obtain the exa
 ct solutions of fully nonlinear Navier-Stokes equations within a thin rota
 ting atmospheric shell that serves as a simple mathematical description of
  an atmospheric circulation caused by the temperature difference between t
 he equator and the poles with included equatorial flows modeling heat wave
 s\, known as Kelvin Waves. Special attention will be given to analyzing an
 d visualizing the conserved densities associated with obtained exact solut
 ions. As another modeling scenario\, the exact solution of the shallow wat
 er equations simulating equatorial atmospheric waves of planetary scales w
 ill be analyzed and visualized.\n
LOCATION:https://researchseminars.org/talk/mmandim/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.L. Mironov\, S.V. Mironov (Institute for physics of microstructu
 res RAS\, Nizhny Novgorod\, Russia)
DTSTART:20231228T110000Z
DTEND:20231228T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/66
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/66/"
 >Sedeonic equations of electromagnetic field. On the question of symmetry 
 between electricity and magnetism</a>\nby V.L. Mironov\, S.V. Mironov (Ins
 titute for physics of microstructures RAS\, Nizhny Novgorod\, Russia) as p
 art of Mathematical models and integration methods\n\n\nAbstract\nWe refor
 mulate the equations of the electromagnetic field in highly symmetric form
  based on the space-time algebra of sedeons. The role of the Lorentz gauge
  condition is discussed in detail and a generalization of the gauge (gradi
 ent) invariance of the electromagnetic field equations is carried out. The
  electrodynamics of Dirac monopoles and Schwinger dyons is considered and 
 the dyonic model of charged particles is discussed.\n\n1. V.L. Mironov\, S
 .V. Mironov\, Sedeonic equations in field theory\, Advances in Applied Cli
 fford Algebras\, 30\, 44 1-26 (2020).\n\n2. V. L. Mironov\, S. V. Mironov\
 , Sedeonic field equations for dyons\, Advances in Applied Clifford Algebr
 as\, 28(3)\, 64 1-17 (2018).\n
LOCATION:https://researchseminars.org/talk/mmandim/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Dorodnitsyn (Keldysh Institute of Applied Mathematics\, M
 oscow\, Russia)
DTSTART:20240118T110000Z
DTEND:20240118T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/67/"
 >Symmetries and conservation laws for differential equations\, difference 
 equations and second-order delay ODEs</a>\nby Vladimir Dorodnitsyn (Keldys
 h Institute of Applied Mathematics\, Moscow\, Russia) as part of Mathemati
 cal models and integration methods\n\n\nAbstract\nThe report is devoted to
  operators identities for Lagrangian and the Hamiltonian\napproach to the 
 connection of symmetries of equations with conservation laws\, and the Lag
 randian\nidentity for equations which have no variational statement. We co
 nsider also difference equations and\nODEs with retarded argument and appr
 opriate operators identities.\n\nThis is based on joint works with Roman K
 ozlov\, Pavel Winternitz\, Sergey Meleshko and Evgenii Kaptsov.\n
LOCATION:https://researchseminars.org/talk/mmandim/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:В.В. Веденяпин\, Н.Н. Фимин\, В.М. Чечет
 кин\, А.Г. Петров (ИПМ им. М.В. Келдыша РАН / 
 ИПМех им. А.Ю. Ишлинского РАН)
DTSTART:20240201T110000Z
DTEND:20240201T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/68
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/68/"
 >Уравнение Власова — Эйнштейна и точки Л
 агранжа</a>\nby В.В. Веденяпин\, Н.Н. Фимин\, В.
 М. Чечеткин\, А.Г. Петров (ИПМ им. М.В. Келды
 ша РАН / ИПМех им. А.Ю. Ишлинского РАН) as part
  of Mathematical models and integration methods\n\n\nAbstract\nВ клас
 сических работах (см. [1]) уравнения для по
 лей предлагаются без вывода правых част
 ей. Здесь мы даем вывод правых частей ура
 внений Максвелла и Эйнштейна в рамках ур
 авнений Власова — Максвелла — Эйнштейн
 а из классического  принципа наименьшег
 о действия [2-4]\, а также их гидродинамиче
 ских и Гамильтон — Якобиевых следствий [
 2-4]. Ускоренное расширение Вселенной\, от
 меченное Нобелевской премией по физике 
 в 2011 году\, вызывает пристальное внимани
 е. Общепринятым объяснением сейчас явля
 ется добавление лямбда-члена Эйнштейна 
 в релятивистское действие. И хорошо изве
 стно\, что в нерелятивистской теории это 
 соответствует добавлению отталкивающег
 о квадратичного потенциала [2-4]. Мы изуча
 ем решение типа Фридмана [2-4] (модель Милн
 а — Маккри) и точки Лагранжа с таким поте
 нциалом [4].\n\n1. Фок В.А. Теория пространст
 ва\, времени и тяготения. М.: ЛКИ\, 2007.\n\n2. В
 еденяпин В.В.\, Воронина М.Ю.\, Руссков А.А. 
 О выводе уравнений электродинамики и гр
 авитации из принципа наименьшего действ
 ия. Доклады РАН\, 2020\, том 495\, с. 9–13.\n\n3. V.V. V
 edenyapin\, N.N. Fimin\, V.M. Chechetkin. The generalized Friedman model a
 s a self–similar solution of Vlasov–Poisson equations system // Europe
 an Physical Journal Plus\, 136\, No 670 (2021).\n\n4. В.В. Веденя
 пин\, В.И. Паренкина\, А.Г. Петров\, Чжан Хао
 чэнь. Уравнение Власова — Эйнштейна и то
 чки Лагранжа // Препринты ИПМ им. М.В.Келд
 ыша. 2022. № 23\, 23 с.\n
LOCATION:https://researchseminars.org/talk/mmandim/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А.В. Велисевич (Сибирский федеральны
 й университет)
DTSTART:20240215T110000Z
DTEND:20240215T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/69
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/69/"
 >Обратные задачи для эллиптических урав
 нений и уравнений соболевского типа</a>\nby
  А.В. Велисевич (Сибирский федеральный ун
 иверситет) as part of Mathematical models and integration methods
 \n\n\nAbstract\nРассматриваются три обратные з
 адачи отыскания неизвестной функции и н
 еизвестного младшего коэффициента в элл
 иптическом уравнении с граничными данны
 ми различного типа и интегральным услов
 ием переопределения на границе исследуе
 мой области. Также исследуются условия с
 табилизации сильного решения обратной з
 адачи для уравнения соболевского типа к 
 решению одной из этих задач. Оператор 𝑀 
 предполагается сильно эллиптическим и с
 амосопряженным.\n\nОсновными результатам
 и работы являются теоремы существования
  и единственности сильного обобщенного 
 решения исходных задач\, а также достато
 чные условия непрерывной зависимости ре
 шений этих задач от исходных данных. Кро
 ме того\, к основным результатам относят
 ся достаточные условия стабилизации сил
 ьного решения обратной задачи для уравн
 ения соболевского типа к сильному решен
 ию соответствующей стационарной обратн
 ой задачи для эллиптического уравнения 
 с интегральным условием переопределени
 я на границе.\n\nСуществование и единстве
 нность доказываются методом\, суть котор
 ого состоит в продолжении данных с грани
 цы в область и сведении обратной задачи 
 к операторному уравнению второго рода\, 
 для неизвестного коэффициента.\n\nПракти
 ческий интерес к данным задачам обуслов
 лен тем фактом\, что в многочисленных при
 ложениях коэффициенты исходного уравне
 ния характеризуют физические свойства с
 реды: проницаемость\, теплопроводность и
  так далее. В рассмотренных задачах неиз
 вестным является коэффициент поглощени
 я.\n
LOCATION:https://researchseminars.org/talk/mmandim/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А.В. Боровских (МГУ)
DTSTART:20240229T110000Z
DTEND:20240229T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/70
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/70/"
 >Геометрия группы Ли в групповом анализе
  одномерного кинетического уравнения</a>\
 nby А.В. Боровских (МГУ) as part of Mathematical models and 
 integration methods\n\n\nAbstract\nГрупповая классифика
 ция одномерных кинетических уравнений (
 о которой рассказывалось в прошлом докл
 аде) и которая выполнялась с целью иссле
 дования возможности установления связи 
 между кинетическими уравнениями и уравн
 ениями сплошной среды с использованием 
 группового подхода\, помимо уравнений с 
 максимальной ($8$-мерной) группой симметр
 ий\, которые эквивалентны уравнению с от
 сутствующим внешним силовым полем\, дала
  еще ряд уравнений с субмаксимальными гр
 уппами симметрий (размерности три). Эти у
 равнения связаны с весьма экзотическими
  силовыми полями\, рассмотрение которых 
 можно было бы считать малоинтересным с т
 очки зрения приложений\, если бы группы с
 имметрий в самых экзотических случаях н
 е оказались бы в точности совпадающими с
  группами движений двумерных (в простран
 стве переменных ($t$\, $x$)) римановых метрик
  постоянной кривизны.\n\nЭто поставило во
 прос о том\, какова геометрическая сторо
 на полученной классификации? Что это озн
 ачает с геометрической точки зрения? Поп
 ытки усмотреть какие-то геометрические 
 интерпретации в остальных субмаксималь
 ных случаях успеха не имели до тех пор\, п
 ока рассмотрения велись в пространстве 
 переменных ($t$\, $x$). Помог здесь достаточн
 о странный\, с точки зрения физики\, сдвиг
  исходных позиций\, состоящий в том\, что 
 геометрия стала рассматриваться не в дв
 умерном\, а в трехмерном пространстве ($t$\
 , $x$\, $c$)\, включающем\, помимо прежних пере
 менных — времени и координаты — еще и ск
 орость.\n\nТакой ход позволил совсем по-др
 угому взглянуть на геометрию. Поскольку 
 размерность рассматриваемого пространс
 тва переменных оказалась совпадающей с 
 размерностью группы\, искомая геометрия 
 автоматически оказывалась и геометрией 
 самой группы. То есть речь пошла уже о то
 м\, возможно ли на самой группе Ли задать 
 риманову геометрию так\, чтобы она была и
 нвариантна относительно этой группы? От
 вет оказался положительный и простой\, т
 акая геометрия задавалась\, как выяснило
 сь\, квадратичной формой с постоянными к
 оэффициентами от $n$ линейных дифференци
 альных форм\, инвариантных относительно 
 той же группы. При этом оказалось\, что дл
 я любой такой квадратичной формы (для лю
 бых коэффициентов) траектории частиц в п
 ространстве переменных ($t$\, $x$\, $c$) являют
 ся спиралями\, то есть имеют постоянную к
 ривизну и кручение. Основную же роль в об
 основании этого факта сыграла алгебра\, 
 которая была названа двойственной\, и ко
 торая определяется условием коммутации 
 с исходной алгеброй. Траектории частиц\, 
 которые были упомянуты выше\, оказываютс
 я траекториями однопараметрических под
 групп этой двойственной алгебры\, и тот ф
 акт\, что эти траектории являются спирал
 ями\, порождает массу вопросов об отноше
 нии этой геометрии к геометрическим кон
 струкциям Э. Картана\, который полагал тр
 аектории однопараметрических групп гео
 дезическими.\n
LOCATION:https://researchseminars.org/talk/mmandim/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Kaptsov (ICM SB RAS\, Krasnoyark\, Russia)
DTSTART:20240314T110000Z
DTEND:20240314T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/71
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/71/"
 >Intermediate systems and invariants</a>\nby Oleg Kaptsov (ICM SB RAS\, Kr
 asnoyark\, Russia) as part of Mathematical models and integration methods\
 n\n\nAbstract\nIn this report some classical and new methods of integratio
 n of partial differential equations are considered. The approaches of Mong
 e and Darboux are briefly described. Examples of the construction of gener
 al solutions of second order equations based on invariants of the characte
 ristics of hyperbolic equations are given. Intermediate systems of partial
  derivative equations are introduced in terms of differential algebra. Equ
 ations possessing intermediate systems are found.\n
LOCATION:https://researchseminars.org/talk/mmandim/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Вячеслав Кузоватов (Сибирский федер
 альный университет)
DTSTART:20240321T110000Z
DTEND:20240321T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/72
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/72/"
 >Дзета-функция корней некоторого класса 
 целых функций и ее свойства</a>\nby Вячесла
 в Кузоватов (Сибирский федеральный унив
 ерситет) as part of Mathematical models and integration methods\n\n
 \nAbstract\nВ докладе будет рассмотрена дзета
 -функция Римана и способ получения функц
 ионального соотношения для нее\, основан
 ный на интегральных представлениях: кла
 ссической формуле Плана и интегральном 
 представлении Бине. Будет введено обобщ
 ение дзета-функции Римана\, а именно дзет
 а-функция корней некоторого класса целы
 х функций\, указана связь с классической 
 дзета-функцией Римана.\n\nОсновным резуль
 татом доклада являются интегральные пре
 дставления для дзета-функции корней\, ан
 алог формулы Плана и формулы Бине. Откры
 тая задача: функциональное уравнение дл
 я дзета-функции корней\, аналогичное фун
 кциональному уравнению для дзета-функци
 и Римана.\n
LOCATION:https://researchseminars.org/talk/mmandim/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:В.Л. Миронов\, С.В. Миронов (Институт ф
 изики микроструктур РАН\, Нижний Новгоро
 д)
DTSTART:20240404T110000Z
DTEND:20240404T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/73
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/73/"
 >Седеонные уравнения для полей с массой 
 кванта\, не равной нулю. Модель барион-ба
 рионного взаимодействия</a>\nby В.Л. Мироно
 в\, С.В. Миронов (Институт физики микростр
 уктур РАН\, Нижний Новгород) as part of Mathematical
  models and integration methods\n\n\nAbstract\nНа основе прос
 транственно-временной алгебры седеонов 
 сформулированы симметричные уравнения 
 для полей с ненулевой массой кванта. Рас
 сматривается обобщение калибровочной (г
 радиентной) инвариантности уравнений с 
 учетом ненулевой массы кванта. Обсуждае
 тся модель взаимодействия точечных бари
 онов.\n\n1. V. L. Mironov\, S. V. Mironov. Sedeonic equations in field
  theory\, Advances in Applied Clifford Algebras\, 30\, 44 1-26 (2020).\n\n
 2. S. V. Mironov\, V. L. Mironov. Sedeonic equations of massive fields // 
 International Journal of Theoretical Physics\, 54(1)\, 153–168 (2015).\n
 \n3. V. L. Mironov\, S. V. Mironov. Gauge invariance of sedeonic equations
  for massive and massless fields\, International Journal of Theoretical Ph
 ysics\, 55\, 3105 (2016).\n
LOCATION:https://researchseminars.org/talk/mmandim/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.E. Adler (Landau Institute for Theoretical Physics)
DTSTART:20240418T110000Z
DTEND:20240418T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/74
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/74/"
 >Negative symmetries: properties and applications</a>\nby V.E. Adler (Land
 au Institute for Theoretical Physics) as part of Mathematical models and i
 ntegration methods\n\n\nAbstract\nOne of the definitions of negative symme
 try of an integrable equation is given by the formula $u_t=(R-a)^{-1}(0)$ 
 where $R$ is the recursion operator and $a$ is a parameter. This extension
  of symmetry algebra is of interest from different points of view: 1) nega
 tive symmetry can be interesting as an independent equation\; 2) it contai
 ns information about the entire integrable hierarchy\, since the expansion
  in parameter a serves as a generating function for higher symmetries\; 3)
  there are applications in the problem of constructing finite-dimensional 
 reductions\, especially in combination with classical symmetries (which pr
 ovides an approach to constructing solutions expressed through higher anal
 ogues of Painlevé transcendents)\; 4) there are connections with other co
 nstructions\, such as squared eigenfunctions symmetries and Bäcklund tran
 sformations. In the talk\, we consider examples related to the KdV\, Bouss
 inesq and Krichever-Novikov equations and the Volterra lattice.\n
LOCATION:https://researchseminars.org/talk/mmandim/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.E. Adler (Landau Institute for Theoretical Physics)
DTSTART:20240425T110000Z
DTEND:20240425T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/75
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/75/"
 >Negative symmetries: properties and applications. Continuation\, part 2</
 a>\nby V.E. Adler (Landau Institute for Theoretical Physics) as part of Ma
 thematical models and integration methods\n\n\nAbstract\nOne of the defini
 tions of negative symmetry of an integrable equation is given by the formu
 la $u_t=(R-a)^{-1}(0)$ where $R$ is the recursion operator and $a$ is a pa
 rameter. This extension of symmetry algebra is of interest from different 
 points of view: 1) negative symmetry can be interesting as an independent 
 equation\; 2) it contains information about the entire integrable hierarch
 y\, since the expansion in parameter a serves as a generating function for
  higher symmetries\; 3) there are applications in the problem of construct
 ing finite-dimensional reductions\, especially in combination with classic
 al symmetries (which provides an approach to constructing solutions expres
 sed through higher analogues of Painlevé transcendents)\; 4) there are co
 nnections with other constructions\, such as squared eigenfunctions symmet
 ries and Bäcklund transformations. In the talk\, we consider examples rel
 ated to the KdV\, Boussinesq and Krichever-Novikov equations and the Volte
 rra lattice.\n
LOCATION:https://researchseminars.org/talk/mmandim/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Б.И. Сулейманов (Институт математики
  с вычислительным центром\, Уфа\, Россия)
DTSTART:20240523T110000Z
DTEND:20240523T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/76
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/76/"
 >Мероморфность решений системы уравнени
 й типа Пенлеве 34\, связанной с негативным
 и симметриями уравнения Кортевега — де 
 Вриза</a>\nby Б.И. Сулейманов (Институт мате
 матики с вычислительным центром\, Уфа\, Р
 оссия) as part of Mathematical models and integration methods\n\n\nAb
 stract\nДоклад посвящен доказательству тог
 о факта\, что  при $t\\neq 0$ все локально голо
 морфные решения системы ОДУ\n$$(y_j)'''_{xxx}=S_j(
 x\,t\,y_j\, u\,(y_j)'_x\, u'_x)=2u'_xy_j+4(u-\\lambda_j)(y_j)'_x\,\\\; (j=
 1\, \\dots\,n)\,$$\nгде $u=\\dfrac{x}{6t}+\\dfrac{1}{3t}\\sum_{j=1}^n y
 _j$ мероморфно продолжимы на всю комплекс
 ную плоскость изменения переменной $x$. Д
 анная система ОДУ при $n=1$ эквивалентна у
 равнению Пенлеве 34 (которое\, в свою очер
 едь\, выражается через решения второго у
 равнения Пенлеве). Она была введена в рас
 смотрение в недавней статье V.$\\\,$E. Adler\, M.$
 \\\,$P. Kolesnikov\, JMP\, 2023. Ей и её связям с негати
 вными симметриям была посвящена часть п
 редыдущего доклада В.$\\\,$Э. Адлера на дан
 ном семинаре.\n
LOCATION:https://researchseminars.org/talk/mmandim/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А. О. Смирнов (Санкт-Петербургский го
 сударственный университет аэрокосмичес
 кого приборостроения)
DTSTART:20240530T110000Z
DTEND:20240530T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/77
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/77/"
 >Различия между решениями скалярных и ве
 кторных интегрируемых нелинейных уравн
 ений с точки зрения теории конечнозонно
 го интегрирования</a>\nby А. О. Смирнов (Санк
 т-Петербургский государственный универ
 ситет аэрокосмического приборостроения
 ) as part of Mathematical models and integration methods\n\nAbstract: TBA\
 n
LOCATION:https://researchseminars.org/talk/mmandim/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.L. Mironov (Institute for physics of microstructures RAS\, Nizhn
 y Novgorod\, Russia)
DTSTART:20240919T090000Z
DTEND:20240919T100000Z
DTSTAMP:20260422T225819Z
UID:mmandim/78
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/78/"
 >Self-consistent hydrodynamic model of plasma. Sound waves in plasma</a>\n
 by V.L. Mironov (Institute for physics of microstructures RAS\, Nizhny Nov
 gorod\, Russia) as part of Mathematical models and integration methods\n\n
 Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/mmandim/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.M. Churilov (Institute of Solar-Terrestrial Physics SB RAS\, Irk
 utsk\, Russia)
DTSTART:20241003T110000Z
DTEND:20241003T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/79
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/79/"
 >Traveling Alfven waves in plasma flows along magnetic field</a>\nby S.M. 
 Churilov (Institute of Solar-Terrestrial Physics SB RAS\, Irkutsk\, Russia
 ) as part of Mathematical models and integration methods\n\n\nAbstract\nIn
  the framework of ideal magnetohydrodynamics\, a one-dimensional problem o
 f linear Alfven waves propagation is considered in a stationary flow of in
 homogeneous plasma along straight uniform magnetic field. Four families of
  flows are found\, in which accelerated and retarded by the flow waves of 
 arbitrary shape can propagate independently of each other\, that is\, with
 out reflection. It is shown that in two of these families both waves have 
 a similar structure\, but in the other two their structures differ signifi
 cantly.\n
LOCATION:https://researchseminars.org/talk/mmandim/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.P. Tsarev (SFU\, Krasnoyarsk\, Russia)
DTSTART:20241017T110000Z
DTEND:20241017T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/80
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/80/"
 >Sparse recovery and Compressive sensing in theory and in practice</a>\nby
  S.P. Tsarev (SFU\, Krasnoyarsk\, Russia) as part of Mathematical models a
 nd integration methods\n\n\nAbstract\nIn the 1990's\, algorithms for solvi
 ng linear systems with the number of equations smaller than the number of 
 unknowns\, provided that among the unknowns there are only a small number 
 of non-zero ones (however\, we do not know which of them are non-zero!) we
 re proposed.\n\nA new stage was opened in the early 2000's by the well-kno
 wn specialist in signal processing David Donoho and the Fields Medal winne
 r Terence Tao and their students. The results in this area were awarded th
 e 2018 Gauss Prize (given by the International Mathematical Union)\, they 
 were reported as plenary talks at the International Congress of Mathematic
 ians\, etc.\n\nAfter the works of Donoho\, Tao and many other researchers\
 , progress in this area was rapid. This research area was called "compress
 ive sensing" or "compressed sensing" (along with the older name "sparse re
 covery").\n\nThe most well-known applications of these results are in sign
 al processing. Particularly noteworthy are applications of sparse recovery
  technologies in magnetic resonance imaging (MRI)\, which reduce the time 
 spend by patients in the MRI machine and improve the quality of the result
 ing image.\n\nThe report will discuss the main ideas of this area and demo
 nstrate a small practical application in the problem of finding jumps in a
  noisy signal.\n
LOCATION:https://researchseminars.org/talk/mmandim/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. B. Borisov and D. V. Dolgikh (M.N. Mikheev Institute of Metal P
 hysics of Ural Branch of Russian Academy of Sciences\, Yekaterinburg\, Rus
 sia)
DTSTART:20241031T110000Z
DTEND:20241031T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/81
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/81/"
 >Symmetries of the classical Heisenberg model</a>\nby A. B. Borisov and D.
  V. Dolgikh (M.N. Mikheev Institute of Metal Physics of Ural Branch of Rus
 sian Academy of Sciences\, Yekaterinburg\, Russia) as part of Mathematical
  models and integration methods\n\n\nAbstract\nThe symmetries of the class
 ical Heisenberg model are examined. It is shown that such symmetries are g
 roups of conformal transformations and rotations. The invariance of vortex
  structures with respect to a group of rotations is studied. The applicati
 on of the found transformations of the group of field rotations to the alr
 eady known solutions of the Heisenberg model (such as instantons\, vortex 
 “targets” and “spirals”) generates other structures\, which are al
 so solutions of this model\, with the properties being determined by the o
 riginal structures.\n\nKeywords: Heisenberg model\, ferromagnet\, vortex\,
  Lee groups\n
LOCATION:https://researchseminars.org/talk/mmandim/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O. V. Kaptsov
DTSTART:20241114T110000Z
DTEND:20241114T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/82
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/82/"
 >Integration  of acoustic wave equations  for inhomogeneous media</a>\nby 
 O. V. Kaptsov as part of Mathematical models and integration methods\n\n\n
 Abstract\nWe obtain exact solutions of the acoustic wave equations for inh
 omogeneous media. Two methods for integrating these equations are proposed
 . The first one is based on the of the Laplace cascade method\, while the 
 second method involves reducing two-dimensional and three-dimensional mode
 ls to the wave equation. In the case of plane waves\, we find new solution
 s  depending on two arbitrary functions. These solutions generalize the cl
 assical ones obtained by Euler. In the two-dimensional and three-dimension
 al cases\, equations that can be reduced to equations with constant coeffi
 cients are found.\n
LOCATION:https://researchseminars.org/talk/mmandim/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. A. Shlapunov (SibFU\, Krasnoyarsk\, Russia)
DTSTART:20241128T110000Z
DTEND:20241128T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/83
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/83/"
 >Maxwell's and Stokes' operators associated with elliptic differential com
 plexes</a>\nby A. A. Shlapunov (SibFU\, Krasnoyarsk\, Russia) as part of M
 athematical models and integration methods\n\n\nAbstract\nWe propose a reg
 ular method for generating consistent systems of partial differential equa
 tions (PDEs) that describe a wide class of models in natural sciences. Suc
 h systems appear within typical constructions of the Homological Algebra a
 s complexes of differential operators describing compatibility conditions 
 for overdetermined PDEs. Additional assumptions on the ellipticity/paramet
 er-dependent ellipticity of the  differential complexes provide a wide ran
 ge of elliptic\, parabolic and hyperbolic operators. In particular\, most 
 equations related to modern Mathematical Physics are generated by the de R
 ham complex of differentials on exterior differential forms. These include
 s the equations based on elliptic Laplace and Lam\\'e type operators\; the
  parabolic heat and mass transfer equations\; the Euler type and Navier-St
 okes type equations in Hydrodynamics\; the hyperbolic wave equation and th
 e Maxwell equations in Electrodynamics\; the Klein-Gordon equation in Rela
 tivistic Quantum Mechanics\; and so on. The advantage of our approach is t
 hat this generation method covers a broad class of generating systems\, es
 pecially in high dimensions\, due to different underlying algebraic struct
 ures than the conventional ones.\n\nThis is joint work with V. L. Mironov 
 and A. N. Polkovnikov.\n
LOCATION:https://researchseminars.org/talk/mmandim/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. V. Nazarenko (Université de Nice Sophia Antipolis: Nice\, Prov
 ence-Alpes-Cote d'Azur\, France)
DTSTART:20241212T110000Z
DTEND:20241212T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/84
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/84/"
 >Universal regimes of turbulence in Bose-Einstein condensation</a>\nby S. 
 V. Nazarenko (Université de Nice Sophia Antipolis: Nice\, Provence-Alpes-
 Cote d'Azur\, France) as part of Mathematical models and integration metho
 ds\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/mmandim/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:А. В. Боровских (МГУ\, Россия)
DTSTART:20241226T110000Z
DTEND:20241226T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/85
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/85/"
 >Метод распространяющихся волн для одно
 мерной неоднородной среды с памятью</a>\nby
  А. В. Боровских (МГУ\, Россия) as part of Mathematica
 l models and integration methods\n\n\nAbstract\nДля уравнения 
 $u_{tt}=u_{xx}$ имеется три канонических спосо
 ба представления общего решения:\n\n— чер
 ез распространяющиеся волны $u=f(x-t)+g(x+t)$\;\n
 \n— формула Даламбера (интеграл от начал
 ьных данных)\;\n\n— в виде ряда Фурье.\n\nВто
 рой и третий способы были распространен
 ы на очень широкие классы уравнений. В на
 иболее абстрактном исполнении метод Фур
 ье сейчас представлен в спектральной те
 ории операторов в различных функциональ
 ных пространствах\, а интегральное предс
 тавление — в виде теории полугрупп. Что 
 же касается первого способа\, то он так и 
 остался исключительной принадлежностью
  простейшего уравнения\, хотя даже для та
 кого уравнения\, как только область\, в ко
 торой оно задано\, оказывается не прямоу
 гольной\, или краевые условия не простей
 шие (Дирихле/Нейман) мы немедленно возвр
 ащаемся к формуле распространяющихся во
 лн. Это порождает естественный вопрос\, н
 ельзя ли построить метод распространяющ
 ихся волн в более общем варианте?\n\nОказы
 вается\, ответ на этот вопрос является по
 ложительным\, по крайней мере в одномерн
 ом случае. В докладе будет дано представ
 ление общего решения для волнового урав
 нения для неоднородной струны и для урав
 нения в одномерной неоднородной среде с 
 памятью через распространяющиеся волны.
  Основной неожиданностью метода распрос
 траняющихся волн здесь является то\, что 
 эти волны не являются решением исходног
 о уравнения. Решение получается только к
 ак сумма. Это объясняет относительную не
 успешность известных методов поиска реш
 ений типа волны в неоднородной среде — к
 аждый раз волны предполагались решением
  исходного уравнения.\n\nОбзор этих резул
 ьтатов представлен в статье:\n\nБоровских
  А.В. Метод распространяющихся волн // Диф
 ференциальные уравнения. - 2023. - Т. 59. - №5. -
  C. 619-634. doi: 10.31857/S0374064123050060 (полный текст см
 . https://istina.msu.ru/download/557753070/1tEucw:8EoRHDe8UC1jm1QVRz4x9QKR
 DM4/ )\n
LOCATION:https://researchseminars.org/talk/mmandim/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.L. Mironov (Institute for physics of microstructures RAS\, Nizhn
 y Novgorod\, Russia)
DTSTART:20250123T110000Z
DTEND:20250123T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/86/"
 >Modified equations of heat transfer and diffusion in solids</a>\nby V.L. 
 Mironov (Institute for physics of microstructures RAS\, Nizhny Novgorod\, 
 Russia) as part of Mathematical models and integration methods\n\n\nAbstra
 ct\nWe discuss heat and mass transfer equations based on modified relation
 ships for heat flux (Fourier's law) and diffusing impurity flux (Fick's la
 w). It is shown that the proposed modification leads to second-order ellip
 tic equations that describe the change in profiles of temperature and impu
 rity concentration with a finite velocity. One-dimensional heat transfer p
 rocesses in plates are considered as an example.\n
LOCATION:https://researchseminars.org/talk/mmandim/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. B. Karmanova (Sobolev Institute of Mathematics\, Novosibirsk\, 
 Russia)
DTSTART:20250206T110000Z
DTEND:20250206T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/87
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/87/"
 >Area Formula for Surfaces in Non-Holonomic Structures</a>\nby M. B. Karma
 nova (Sobolev Institute of Mathematics\, Novosibirsk\, Russia) as part of 
 Mathematical models and integration methods\n\n\nAbstract\nNonholonomic st
 ructures can be considered as a natural generalization of the structures o
 f Riemannian geometry. One of their main features is a specific metric\, r
 elative to which one can traverse distances of different orders along diff
 erent directions ($t$\, $t^2$\, $t^3$\, etc.) in time $t$. Therefore\, map
 pings that are Lipschitz in the classical sense are generally not such in 
 the nonholonomic sense\, and vice versa. Nevertheless\, in the second half
  of the 20th century\, the theory of sub-Riemannian differentiability was 
 created\, which allows one to approximate "complicated" mappings by regula
 r ones. Carnot groups are one of the well-known examples of nonholonomic s
 tructures. The talk will discuss the sub-Riemannian analogue of the area f
 ormula for surfaces obtained under intrinsically Lipschitz mappings of ope
 n sets of Carnot groups. Such groups and their generalizations\, Carnot ma
 nifolds\, arise naturally in both theoretical and applied fields\, such as
  neurobiology\, robotics\, and astrodynamics.\n
LOCATION:https://researchseminars.org/talk/mmandim/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.V. Lopatin (Federal Research Center for Information and Computat
 ional Technologies\, Novosibirsk\, Russia)
DTSTART:20250220T110000Z
DTEND:20250220T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/88
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/88/"
 >Model and bending analysis of sandwich beam with composite facings and co
 mpressible orthotropic core using Abramov’s sweep method</a>\nby A.V. Lo
 patin (Federal Research Center for Information and Computational Technolog
 ies\, Novosibirsk\, Russia) as part of Mathematical models and integration
  methods\n\n\nAbstract\nModern sandwich structures are employed in a broad
  range of aerospace\, marine and civil structural applications. They are e
 fficient and lightweight constructions with high bending stiffness\, high 
 strength\, and high buckling resistance. Such modern sandwich structures a
 re combination of composite facings with a lightweight core layer. The fac
 ings carry the tensile and compressive loads\, while the core transmits sh
 ear loads and serves to hold the facings in positions\, which maximize the
  flexural stiffness of the structure. Therefore\, the general structural r
 esponse of a sandwich structure is an action\, consisting of couple\, comp
 ression or tension stress resultants in the facings and shear stresses alo
 ng with vertical normal stresses within the core. Note that\, in such stru
 ctures\, the facings may undergo different displacements due to the compre
 ssible core that may change its height. Proper reflection of this effect i
 n the strain-stress analysis would require the application of the advanced
  modeling and computational techniques and approaches.\n\nIn this study th
 e new computational model of sandwich beam is developed. The beam one-dime
 nsional model by virtue of its relative simplicity is useful for prelimina
 ry analyses of the more complicated two-dimensional sandwich structures. T
 he model for the facings was built based on the traditional hypotheses tha
 t allow a transverse shear deformation to be taken into account. The defor
 mation model created for the elastic orthotropic core is original. This mo
 del considers a non-linear character of variation of the transverse and ax
 ial displacements over the thickness of core. Governing system of differen
 tial equations\, describing join deformation of facings and core\, was der
 ived using static and kinematic contact conditions between these parts of 
 the structure. System of governing differential equations has 14th order. 
 Numerical analysis of the stress-strain state of the sandwich beam for var
 ious loading cases and boundary conditions has been performed. System of d
 ifferential equations\, together with the corresponding boundary condition
 s\, represented the boundary value problem that was solved using Abramov
 ’s sweep method. Finite element modeling of the sandwich beam was execut
 ed using the FEM software package MSC Nastran® and the results were compa
 red with the developed theory. The computational model of deformation of t
 he sandwich beam and method of its analysis developed in this study provid
 e an opportunity to investigate a strong oscillating behavior of the compo
 nents of stress-strain state of the structure under consideration. This al
 lows the results of analyses performed to be used for the verification of 
 solutions for similar problems found using numerical techniques\, includin
 g the finite element method.\n\nThis is joint work with A.E. Burov (Federa
 l Research Center for Information and Computational Technologies) and E.A.
  Lopatin (Steklov Mathematical Institute of the Russian Academy of Science
 s).\n
LOCATION:https://researchseminars.org/talk/mmandim/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kostya Druzhkov (Department of Mathematics and Statistics\, Univer
 sity of Saskatchewan\, Saskatoon\, Canada)
DTSTART:20250306T123000Z
DTEND:20250306T133000Z
DTSTAMP:20260422T225819Z
UID:mmandim/89
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/89/"
 >Invariant reduction for partial differential equations: conservation laws
 </a>\nby Kostya Druzhkov (Department of Mathematics and Statistics\, Unive
 rsity of Saskatchewan\, Saskatoon\, Canada) as part of Mathematical models
  and integration methods\n\n\nAbstract\nAmong various methods for construc
 ting exact solutions of partial differential equations\, the symmetry appr
 oach is particularly noteworthy. It turns out that systems describing inva
 riant solutions inherit many invariant geometric structures\, even in the 
 case of higher symmetries. In the talk\, we will discuss how invariant con
 servation laws of systems with two independent variables give rise to cons
 tants of invariant motion. The procedure involved is algorithmic for syste
 ms of evolution equations.\n\nThis is joint work with Alexei Cheviakov.\n
LOCATION:https://researchseminars.org/talk/mmandim/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. V. Meleshko (Suranaree University of Technology\, Nakhon Ratcha
 sima\, Thailand)
DTSTART:20250320T110000Z
DTEND:20250320T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/90
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/90/"
 >Equivalence to the classical heat equation through reciprocal transformat
 ions</a>\nby S. V. Meleshko (Suranaree University of Technology\, Nakhon R
 atchasima\, Thailand) as part of Mathematical models and integration metho
 ds\n\n\nAbstract\nThis paper investigates the equivalence of parabolic par
 tial differential equations to the classical\none-dimensional heat equatio
 n using reciprocal transformations. The equations are assumed to be autono
 mous\, and the methodology applied is similar to S. Lie’s approach to so
 lving the linearization problem of second-order ordinary differential equa
 tions. The research is structured in two main parts. In the first part\, n
 ecessary constraints on the class of parabolic partial differential equati
 ons with two independent variables\, which are equivalent to the classical
  heat equation under a reciprocal transformation\, are identified. In the 
 second part\, the remaining conditions are examined\, and sufficient condi
 tions are derived. The corresponding differential equations are then obtai
 ned. All possible cases that arise are thoroughly analyzed\, and the theor
 y is illustrated with several examples.\n\nThis is joint work with P. Siri
 wat (Thailand) and S. R. Svirshchevskii (Russia).\n
LOCATION:https://researchseminars.org/talk/mmandim/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir L. Saveliev (Fesenkov Astrophysical Institute\, Almaty\, 
 Kazakhstan)
DTSTART:20250403T110000Z
DTEND:20250403T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/91
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/91/"
 >Kinetic equation of turbulence from the Boltzmann equation</a>\nby Vladim
 ir L. Saveliev (Fesenkov Astrophysical Institute\, Almaty\, Kazakhstan) as
  part of Mathematical models and integration methods\n\n\nAbstract\nWe hav
 e shown how the kinetic equation for the velocity distribution function of
  an ensemble of turbulent velocities can be rigorously obtained from the B
 oltzmann kinetic equation with the classical collision integral. Compared 
 to the Boltzmann equation on the left-hand side\, the resulting kinetic eq
 uation of turbulence contains ten additional terms. Also\, instead of the 
 frequency of molecular collisions\, the collision integral in the kinetic 
 equation of turbulence includes the collision frequency\, which is signifi
 cantly less than the frequency of molecular collisions. There are two key 
 steps we have undertaken in obtaining the kinetic equation of turbulence. 
 First\, we used the invariance of the collision integral of the Boltzmann 
 equation with respect to the Gaussian transformations. Second\, we introdu
 ced the idea of fragmentation of turbulent flows into turbulent fluid quas
 iparticles. Each such quasiparticle is described by an equilibrium distrib
 ution of molecular velocities with fluctuating mean velocity. Also\, each 
 quasiparticle is characterized by its size\, which is in the range of leng
 th scales larger than the mean free path of molecules and less than the ty
 pical length of spatial variation in the turbulence distribution function.
 \n\n[1] Phys. Fluids 36\, 125175 (2024)\; doi: 10.1063/5.0242731\n
LOCATION:https://researchseminars.org/talk/mmandim/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:В. И. Кузоватов (Сибирский Федеральн
 ый Университет)
DTSTART:20250417T110000Z
DTEND:20250417T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/92
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/92/"
 >Об одном обобщении формулы Бине</a>\nby В. И
 . Кузоватов (Сибирский Федеральный Униве
 рситет) as part of Mathematical models and integration methods\n\n\n
 Abstract\nКлассическая формула Бине выражае
 т значение логарифмической производной 
 $\\Gamma$-функции Эйлера через некоторое инт
 егральное представление. Данный доклад 
 будет посвящен получению обобщения данн
 ого результата. А именно\, получено интег
 ральное представление для логарифмичес
 кой производной целой функции конечного
  порядка (меньше $1/2$) с нулями\, которые об
 разуют некоторую последовательность це
 лых отрицательных чисел. Доказательство
  основано на использовании классической
  формулы суммирования Плана и решении од
 ной интерполяционной задачи. Полученный
  результат может быть использован при по
 лучении функционального соотношения дл
 я дзета-функции корней\, аналогичного фу
 нкциональному уравнению для классическ
 ой дзета-функции Римана.\n
LOCATION:https://researchseminars.org/talk/mmandim/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. V. Shmidt (Institute of computational modelling SB RAS\, Krasno
 yarsk\, Russia)
DTSTART:20250430T110000Z
DTEND:20250430T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/93
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/93/"
 >About one method for solving boundary-value problems arising in free turb
 ulence</a>\nby A. V. Shmidt (Institute of computational modelling SB RAS\,
  Krasnoyarsk\, Russia) as part of Mathematical models and integration meth
 ods\n\n\nAbstract\nAn approximate solution of the boundary-value problem f
 or a semi-empirical model of the far momentumless turbulent wake is constr
 ucted matching asymptotic expansion of the solution at the boundary of the
  wake with the power series expansion of the solution near its axis. A val
 ue of the self-similarity parameter of the problem is determined during ma
 tching procedure. Maximum error between constructed solution and numerical
  solution does not exceed $0.3\\\,\\%$.\n
LOCATION:https://researchseminars.org/talk/mmandim/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Raskovalov (Institute of Metal Physics UB RAS\, Ekaterinburg\, 
 Russia)
DTSTART:20250515T110000Z
DTEND:20250515T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/94
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/94/"
 >Nonlinear excitations in magnets with a spiral and stripe domain structur
 e</a>\nby A. Raskovalov (Institute of Metal Physics UB RAS\, Ekaterinburg\
 , Russia) as part of Mathematical models and integration methods\n\n\nAbst
 ract\nThe new analytical solutions of the basis magnetism models (the Land
 au–Lifshitz and sine-Gordon equations) are found. They describe quasi-on
 e-dimensional solitons on the periodic background\, that is\, in the strip
 e domain structure of one- and two-axis ferromagnets and in the spiral str
 ucture of magnets without inversion center. The basis investigation method
  is the “dressing technique” – modification of the inverse scatterin
 g problem\, based on the Riemann problem of functions of a complex variabl
 e. The detailed analysis of the obtained solutions is presented. The possi
 bilities to excite and detect the solitons on the experiments are discusse
 d.\n
LOCATION:https://researchseminars.org/talk/mmandim/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. Kiselev (Intitute of Metal Physics UB RAS\, Ekaterinburg\, Russ
 ia)
DTSTART:20250529T110000Z
DTEND:20250529T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/95
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/95/"
 >Nonlinear dynamics of the bulk magnetostatic and exhange-dipole modes in 
 the ferromagnetic plate</a>\nby V. Kiselev (Intitute of Metal Physics UB R
 AS\, Ekaterinburg\, Russia) as part of Mathematical models and integration
  methods\n\n\nAbstract\nEffective equations of the Davey-Stewartson type a
 re obtained by the multiscale expansion technique\, that describe evolutio
 n of the three-dimensional magnetostatic excitations in the ferromagnetic 
 plate. The proposed approach admits generalization. It is shown\, that in 
 the ferromagnetic plates with thickness more than the exchange length evol
 ution of the three-dimensional exchange-dipole wave packets is also descri
 bed by the Davey-Stewartson equations. The threshold values of instability
  of the plane monochromatic waves are calculated. The modulational instabi
 lity of such waves leads to the formation of coherent  structures. The con
 ditions of the formation and explicit solutions for plane soliton excitati
 ons are found. In the framework of the proposed model\, the possibility of
  the critical collapse of the space localized two-dimensional wave structu
 res is predicted.\n
LOCATION:https://researchseminars.org/talk/mmandim/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Borisov (Institute of Metal Physics UB RAS\, Ekaterinburg\, Rus
 sia)
DTSTART:20250612T110000Z
DTEND:20250612T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/96
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/96/"
 >Vortex lattices in two-dimensional ferromagnetics</a>\nby A. Borisov (Ins
 titute of Metal Physics UB RAS\, Ekaterinburg\, Russia) as part of Mathema
 tical models and integration methods\n\n\nAbstract\nWe have integrated the
  two-dimensional Heisenberg model using classical differential geometry me
 thods. Following a hodograph transformation\, the model equations have bee
 n stated in terms of a metric tensor and its derivatives in a curvilinear 
 coordinate system. A general solution of the Heisenberg model in a non-ort
 hogonal coordinate system is found\, when the metric tensor depends on two
  variables. New types of different vortex lattices in a two-dimensional fe
 rromagnet are predicted and analyzed.\n\nThis is joint work with D. Dolgih
 .\n
LOCATION:https://researchseminars.org/talk/mmandim/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O. Kaptsov (FRC ICT\, Novosibirsk\, Russia)
DTSTART:20250925T110000Z
DTEND:20250925T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/97
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/97/"
 >Solutions to the equations of acoustics of inhomogeneous media and gas dy
 namics</a>\nby O. Kaptsov (FRC ICT\, Novosibirsk\, Russia) as part of Math
 ematical models and integration methods\n\n\nAbstract\nThis paper consider
 s one-dimensional equations of acoustics equations of inhomogeneous media 
 and the system of gas dynamics equations with constant entropy. Using the 
 Riemann approach\, the gas dynamics equations are reduced to a second-orde
 r linear hyperbolic equation with variable coefficients. Solutions to this
  equation are constructed using Euler–Darboux transformations. This allo
 ws us to find new exact solutions of the equations of acoustics and gas dy
 namics\, depending on two arbitrary functions.\n
LOCATION:https://researchseminars.org/talk/mmandim/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Makarenko (Lavrentyev Institute of Hydrodynamics\, Novosibirsk\
 , Russia)
DTSTART:20251009T110000Z
DTEND:20251009T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/98
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/98/"
 >Nonlinear interaction of the cylinder with free boundaries and interfaces
 </a>\nby N. Makarenko (Lavrentyev Institute of Hydrodynamics\, Novosibirsk
 \, Russia) as part of Mathematical models and integration methods\n\n\nAbs
 tract\nThe problem of unsteady motion of a cylinder in a deep ideal fluid 
 is considered. The reduction of the initial boundary value problem for the
  Euler equations to a system of nonlinear boundary integral-differential e
 quations is used. Asymptotic solutions are constructed\, that describe the
  early stage of a non-stationary flow that forms when a body accelerates f
 rom rest.\n
LOCATION:https://researchseminars.org/talk/mmandim/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. I. Kuzovatov (Siberian Federal University\, Krasnoyarsk\, Russi
 a)
DTSTART:20251023T110000Z
DTEND:20251023T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/99
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/99/"
 >On determining the number of real zeros of a system of entire functions u
 sing computer algebra methods</a>\nby V. I. Kuzovatov (Siberian Federal Un
 iversity\, Krasnoyarsk\, Russia) as part of Mathematical models and integr
 ation methods\n\n\nAbstract\nВ докладе речь пойдет о с
 оздании инструментария для определения 
 числа вещественных нулей системы целых 
 функций многих комплексных переменных. 
 Методология исследования базируется на 
 том\, что\, при определенных ограничениях
 \, число вещественных нулей такой систем
 ы совпадает с числом вещественных нулей 
 ее результанта. В работе приводится алго
 ритм\, вычисляющий число вещественных ну
 лей результанта системы. Для этого вычис
 ляются степенные суммы результанта сист
 емы и исследуется ганкелева матрица\, со
 ставленная из них. Алгоритм реализован в
  системе компьютерной алгебры Maple. Преим
 ущество предлагаемого подхода к нахожде
 нию числа вещественных нулей системы це
 лых функций состоит в том\, что он позвол
 яет определять это число\, не вычисляя са
 мих нулей. Полученные результаты могут н
 айти применение в различных прикладных 
 задачах\, например\, в  задаче определени
 я числа стационарных состояний системы 
 дифференциальных уравнений химической 
 кинетики.\n
LOCATION:https://researchseminars.org/talk/mmandim/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:K. Druzhkov (University of Saskatchewan\, Saskatoon\, Canada)
DTSTART:20251106T123000Z
DTEND:20251106T133000Z
DTSTAMP:20260422T225819Z
UID:mmandim/100
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/100/
 ">General mechanism of invariant reduction and Noether's theorem</a>\nby K
 . Druzhkov (University of Saskatchewan\, Saskatoon\, Canada) as part of Ma
 thematical models and integration methods\n\n\nAbstract\nGiven a local (po
 int\, contact\, or higher) symmetry of a system of partial differential eq
 uations\, one can consider the system that describes the invariant solutio
 ns (the invariant system). It seems natural to expect that the invariant s
 ystem inherits symmetry-invariant geometric structures in a specific way. 
 We propose a mechanism of reduction of symmetry-invariant geometric struct
 ures\, which relates them to their counterparts on the respective invarian
 t systems. This mechanism covers conservation laws\, the stationary action
  principle\, presymplectic structures\, and more. In particular\, a versio
 n of Noether's theorem naturally arises for systems that describe invarian
 t solutions.\n\nThis is joint work with A. Cheviakov.\n
LOCATION:https://researchseminars.org/talk/mmandim/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.M. Churilov (Institute of Solar-Terrestrial Physics SB RAS\, Irk
 utsk\, Russia)
DTSTART:20251120T110000Z
DTEND:20251120T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/101
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/101/
 ">Traveling waves as solutions of factorized hyperbolic equation</a>\nby S
 .M. Churilov (Institute of Solar-Terrestrial Physics SB RAS\, Irkutsk\, Ru
 ssia) as part of Mathematical models and integration methods\n\n\nAbstract
 \nWe consider the solutions of a 1D linear factorized second-order hyperbo
 lic equation that describes the wave propagation in an inhomogeneous movin
 g medium. The necessary and sufficient condition is found under which both
  waves propagate independently\, that is\, without reflection. Possible va
 riants of wave structure are described.\n
LOCATION:https://researchseminars.org/talk/mmandim/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.M. Kamchatnov (Institute of Spectroscopy Russian Academy of Scie
 nces\, Moscow\, Russia)
DTSTART:20251204T110000Z
DTEND:20251204T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/102
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/102/
 ">Asymptotic integrability of nonlinear wave equations</a>\nby A.M. Kamcha
 tnov (Institute of Spectroscopy Russian Academy of Sciences\, Moscow\, Rus
 sia) as part of Mathematical models and integration methods\n\n\nAbstract\
 nThe notion of asymptotic integrability is based on the asymptotic theory 
 of propagation of high-frequency wave packets along large-scale and time-d
 ependent backgrounds. We assume that the evolution of the background obeys
  the dispersionless (hydrodynamic) limit of the nonlinear wave equation un
 der consideration and demand that the Hamilton equations for the packet's 
 propagation have an additional integral of motion independently of the ini
 tial conditions for the background dynamics. This condition is studied for
  systems described by one or two wave variables\, and it is shown that it 
 imposes strong restrictions on the dispersion relation for linear harmonic
  waves in the case of two wave variables. Existence of the integral of Ham
 ilton’s equations leads to important consequences: (1) it allows one to 
 calculate the number of solitons produced from an intensive initial pulse\
 ; (2) this formula can be generalized in a natural way to the Bohr-Sommerf
 eld quantization rule for parameters of solitons produced from such a puls
 e\; (3) if the condition of asymptotic integrability is only fulfilled app
 roximately\, then the Bohr-Sommerfeld rule provides the solitons’ parame
 ters with good accuracy even for not completely integrable equations\; (4)
  if it is fulfilled exactly\, then the appearing in the theory integral ca
 n be identified with the quasiclassical limit of one of the equations of t
 he Lax pair for the corresponding completely integrable equation with the 
 same dispersion relation and equations of the dispersionless limit\, moreo
 ver\, the second equation of the Lax pair is related to the phase velocity
  of linear waves\; (5) “quantization” of the quasiclassical limit allo
 ws one to restore the full expressions for the Lax pair equations\; (6) an
 alytical continuation of the integral into the complex plane of wave numbe
 rs yields the expression for the soliton’s inverse half-width as a funct
 ion of the background wave variables\; (7) existence of such an integral f
 or soliton motion leads to formulation of Hamiltonian dynamics of solitons
  moving along not-uniform and time-dependent background. The theory is ill
 ustrated by examples\, and it is confirmed by comparison with numerical si
 mulations.\n
LOCATION:https://researchseminars.org/talk/mmandim/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S.M. Sitnik (Belgorod State University\, Russia)
DTSTART:20251218T110000Z
DTEND:20251218T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/103
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/103/
 ">On generalizations of discrete and integral Cauchy–Bunyakovsky inequal
 ities by the method of mean values. Some applications</a>\nby S.M. Sitnik 
 (Belgorod State University\, Russia) as part of Mathematical models and in
 tegration methods\n\n\nAbstract\nIn talk we consider generalizations of di
 screte and integral Cauchy–Bunyakovsky inequalities by the method of mea
 n values with some applications. Mostly the material is compiled as a shor
 t survey\, but some results are proved. Main results are listed\, includin
 g an interesting inequality with maximum and minimum values. Some applicat
 ions are considered from different fields of mathematics. Among them are e
 stimates for some special functions\, including Euler gamma and incomplete
  gamma function\, the Legendre complete elliptic integrals of the first ki
 nd. Also some further possible generalizations are considered and outlined
 \, including generalizations of the Acz´el and Minkovskii inequalities\, 
 a case of spaces with sign–indefinite form\, the Jackson’s 𝑞-integr
 als\, and some others.\n
LOCATION:https://researchseminars.org/talk/mmandim/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:E. N. Pelinovsky (International Laboratory of Dynamical Systems an
 d Applications(HSE Nizhny Novgorod)\, Russia)
DTSTART:20260122T110000Z
DTEND:20260122T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/104
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/104/
 ">Soliton turbulence and rogue waves in systems described by Korteweg–de
  Vries type equations</a>\nby E. N. Pelinovsky (International Laboratory o
 f Dynamical Systems and Applications(HSE Nizhny Novgorod)\, Russia) as par
 t of Mathematical models and integration methods\n\n\nAbstract\nСолит
 онный газ (солитонная турбулентность) яв
 ляется предметом интенсивных исследова
 ний из-за его большой важности для многи
 х физических систем. Обычно этот термин 
 используется для интегрируемых моделей\
 , где солитоны взаимодействуют упруго. О
 днако солитонная турбулентность может б
 ыть также частью неинтегрируемой динами
 ки\, где могут существовать долгоживущие
  решения в виде почти солитонов.\n\nВ наст
 оящем докладе представлены результаты п
 о исследованию солитонной турбулентнос
 ти в рамках уравнений типа Кортевега – д
 е Вриза: как в интегрируемых моделях (кла
 ссическое уравнение Кортевега – де Вриз
 а\, модифицированное уравнение Кортевег
 а – де Вриза\, уравнение Гарднера)\, так и 
 в рамках неинтегрируемых на примере ура
 внения Шамеля\, нелинейный член которого
  содержит модуль волновой функции. Некот
 орые важные статистические характерист
 ики (функции распределения\, моменты и т. 
 д.) рассчитаны численно для однополярных
  и разнополярных солитонных газов. Динам
 ика однополярных газов оказалось очень 
 похожей в случае интегрируемых и неинте
 грируемых моделей. Однако неупругое вза
 имодействие разнополярных солитонов пр
 иводит к передаче энергии от меньших сол
 итонов к большим в рамках неинтегрируем
 ых моделей. С увеличением числа разнопол
 ярных солитонов в волновой системе этот 
 эффект передачи энергии от меньшего сол
 итона к большему\, а также возникновение 
 дисперсионных волн при каждом взаимодей
 ствии солитонов приводит к существенном
 у увеличению эксцесса (четвертого стати
 стического момента)\, который в интегрир
 ованных системах оставался бы квази-ста
 ционарным. Демонстрируется возможность 
 образования аномально больших импульсо
 в в результате эволюции таких волновых п
 олей.\n\nThis is joint work with E. G. Didenkulova.\n
LOCATION:https://researchseminars.org/talk/mmandim/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. Mironov (Institute for physics of microstructures RAS\, Nizhny 
 Novgorod\, Russia)
DTSTART:20260205T110000Z
DTEND:20260205T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/105
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/105/
 ">Wind profiles in atmospheric boundary layer</a>\nby V. Mironov (Institut
 e for physics of microstructures RAS\, Nizhny Novgorod\, Russia) as part o
 f Mathematical models and integration methods\n\n\nAbstract\nWe propose an
  analytical algebraic model of a turbulent boundary layer based on the equ
 ations for vortex flow\, which take longitudinal motion and rotation of vo
 rtex tubes into account. In case of plane turbulent flows this model allow
 s one to calculate the mean velocity distributions in boundary layers unde
 r various conditions. In particular\, we verify proposed model by comparis
 on with the experimental profiles measured in the wind tunnel as well as b
 y fitting of experimental low-level jets profiles measured in atmospheric 
 boundary layer. In all considered cases the calculated model profiles demo
 nstrate good agreement with experimental data.\n
LOCATION:https://researchseminars.org/talk/mmandim/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. P. Kiselev (St. Petersburg Department of V.A.Steklov Institute 
 of Mathematics of the Russian Academy of Sciences)
DTSTART:20260219T110000Z
DTEND:20260219T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/106
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/106/
 ">Solutions of the wave equation with arbitrary functions: relatively undi
 storted waves</a>\nby A. P. Kiselev (St. Petersburg Department of V.A.Stek
 lov Institute of Mathematics of the Russian Academy of Sciences) as part o
 f Mathematical models and integration methods\n\n\nAbstract\nSolutions of 
 the wave equation containing arbitrary functions have attracted the attent
 ion of researchers since the 18th century to the present day. Four such so
 lutions and some of their applications will be discussed.\n
LOCATION:https://researchseminars.org/talk/mmandim/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O. V. Kaptsov (Federal Research Center for Information and Computi
 ng Technologies\, Novosibirsk\, Russia)
DTSTART:20260305T110000Z
DTEND:20260305T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/107
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/107/
 ">Solutions to three-dimensional steady-state gas dynamics equations</a>\n
 by O. V. Kaptsov (Federal Research Center for Information and Computing Te
 chnologies\, Novosibirsk\, Russia) as part of Mathematical models and inte
 gration methods\n\n\nAbstract\nThis paper examines the three-dimensional s
 tationary equations of a polytropic gas and employs symmetry methods to co
 nstruct exact analytical solutions. In the Chaplygin gas case\, the analys
 is yields a highly general solution family depending on three arbitrary fu
 nctions\, while the general adiabatic index formulation admits explicit so
 lutions parameterized by several constants.\n
LOCATION:https://researchseminars.org/talk/mmandim/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A.E. Kulagin (Tomsk Polytechnic University\, Tomsk\, Russia. V.E. 
 Zuev Institute of Atmospheric Optics\, Tomsk\, Russia.)
DTSTART:20260326T110000Z
DTEND:20260326T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/108
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/108/
 ">Solutions to the nonlinear Schrodinger equation with an anti-Hermitian t
 erm\, localized on curves\, and quasi steady vortex states</a>\nby A.E. Ku
 lagin (Tomsk Polytechnic University\, Tomsk\, Russia. V.E. Zuev Institute 
 of Atmospheric Optics\, Tomsk\, Russia.) as part of Mathematical models an
 d integration methods\n\n\nAbstract\nSpeaking about semiclassically locali
 zed solutions to the Schrödinger equation\, we mean the class of asymptot
 ic solutions that are obtained for the linear Schrödinger equation by the
  Maslov complex germ method [1\,2\,3]. Such solutions are localized in a n
 eighbourhood of the trajectory in the phase space (point for any fixed tim
 e) that is determined by solutions to the Hamilton system (classical equat
 ions). Such approach was also generalized for nonlinear equations [4].\nIn
  our report\, we consider the Cauchy problem where the solutions to the Sc
 hrödinger equation with a nonlocal nonlinearity are localized in a neighb
 orhood of the evolving curve. Also\, we add the anti-Hermitian terms that 
 allows us to consider the dissipative effects. Such problem is solved usin
 g the transition to the space of variables of higher dimension\, where we 
 can apply elements of the Maslov complex germ method. Asymptotic solutions
  to the original problem are the projection of the solutions in the extend
 ed space to the original space. The formalism proposed becomes applicable 
 to the problem of the vortex lattice formation in condensed media with col
 lective excitations. It is shown that such process includes the semiclassi
 cal stage that is treated as the quasi steady vortex state. The evolution 
 of such states is mainly determined by the slow deformation of the semicla
 ssical localization curve. The report is based on the paper [5].\n\nThis i
 s joint work with A.V. Shapovalov.\n\n[1] V.P. Maslov\, The Complex WKB Me
 thod for Nonlinear Equations (I. Linear Theory. Birkhauser Verlag\, Basel\
 , 1994).\n\n[2] V.V. Belov\, S.Y. Dobrokhotov\, Semiclassical Maslov asymp
 totics with complex phases. I. General approach. Theor. Math. Phys. 92(2)\
 , 843–868 (1992).\n\n[3] V.G. Bagrov\, V.V. Belov\, A.Y. Trifonov\, Semi
 classical trajectory-coherent approximation in quantum mechanics I. High-o
 rder corrections to multidimensional time-dependent equations of Schrödin
 ger type. Ann. Phys. 246(2)\, 231–290 (1996).\n\n[4] V.V. Belov\, A.Y. T
 rifonov\, A.V. Shapovalov\, The trajectory-coherent approximation and the 
 system of moments for the Hartree type equation. Int. J. Math. Math. Sci. 
 32(6)\, 325–370 (2002).\n\n[5] Kulagin\, A.\, Shapovalov\, A. Semiclassi
 cal states localized on a one-dimensional manifold and governed by the non
 local NLSE with an anti-Hermitian term. Eur. Phys. J. Plus 141\, 14 (2026)
 . https://doi.org/10.1140/epjp/s13360-025-07236-6\n
LOCATION:https://researchseminars.org/talk/mmandim/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. A. Gordin (National Research University "Higher School of Econo
 mics"\, Hydrometeorological Research Center of the Russian Federation\, Mo
 scow Institute of Physics and Technology\, Innopolis University)
DTSTART:20260402T110000Z
DTEND:20260402T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/109
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/109/
 ">The compact finite-difference scheme and modified Richardson extrapolati
 on for NLSE</a>\nby V. A. Gordin (National Research University "Higher Sch
 ool of Economics"\, Hydrometeorological Research Center of the Russian Fed
 eration\, Moscow Institute of Physics and Technology\, Innopolis Universit
 y) as part of Mathematical models and integration methods\n\n\nAbstract\nA
  compact finite-difference scheme combined with predictor-corrector approa
 ch for solving quasilinear partial differential equations and systems is p
 resented. The nonlinear Schrödinger equation (NLSE) serves as a model pro
 blem to demonstrate the method’s capabilities. The proposed algorithm ac
 hieves fourth-order spatial accuracy and second-order temporal accuracy wh
 ile maintaining computational efficiency through linearization via Newton 
 — Raphson iterations. As a rule\, one iteration is sufficient. The schem
 e was optimized according to the Courant parameter based on the criterion:
  the ratio of computational complexity to solution accuracy.\n\nAlso\, we 
 introduce a modified two-dimensional and quasi-two-dimensional Richardson 
 extrapolation technique that further enhances accuracy up to eighth-order.
 \n\nNumerical experiments confirm the scheme’s high precision and stabil
 ity across a range of Courant parameters as well as a good conservation of
  many first integrals of NLSE. The method is applicable to arbitrary smoot
 h initial data and various boundary conditions. We tested its properties o
 n various solutions (solitons\, collision of several solitons\, chains\, s
 hort-wave noise). In the latter two cases\, there is an alternation of cha
 otic and ordered types of solution behavior.\n\nThis is joint work with D.
  P. Milutin.\n
LOCATION:https://researchseminars.org/talk/mmandim/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. V. Slunyaev (A.V. Gaponov-Grekhov Institute of Applied Physics 
 of the Russian Academy of Sciences\,Nizhny Novgorod\, Russia)
DTSTART:20260409T110000Z
DTEND:20260409T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/110
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/110/
 ">On the self-similar character of rogue waves</a>\nby A. V. Slunyaev (A.V
 . Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of S
 ciences\,Nizhny Novgorod\, Russia) as part of Mathematical models and inte
 gration methods\n\n\nAbstract\nRogue waves are unexpectedly high waves whi
 ch occur seemingly without a reason on a background of waves of the modera
 te amplitude. Most frequently\, they are associated with the action of the
  nonlinear modulational instability of uniform waves with respect to weak 
 long perturbations\, and are considered within the frameworks of the nonli
 near Schrödinger equation (NLSE). So-called Peregrine breathers\, which a
 re exact solutions of the NLSE\, are considered to be the simplest mathema
 tical prototypes of rogue waves. Other types of NLSE breather solutions ar
 e also known (named after E.A. Kuznetsov and N.N. Akhmediev). It should be
  noted that breather solutions have always been obtained either within the
  framework of the Inverse Scattering Technique or as a result of abstract 
 mathematical constructions.\n\nWe discuss that from the general viewpoint\
 , the shape of the most amplified due to the modulational instability enve
 lope should possess a general form. Even more\, the breather solutions are
  shown to be represented by fully coherent perturbations with self-similar
  shapes. The evolving modulations are characterized by constant values of 
 the similarity parameter of the equation (i.e.\, the nonlinearity to dispe
 rsion ratio)\, just like classic solitons. Thus\, breather solutions acqui
 re a clear physical interpretation that is not based on the integrability 
 property of the model. Approximate analytic breather-type solutions are ob
 tained for non-integrable versions of the NLSE with different orders of no
 nlinearity. They are verified by the direct numerical simulation of the mo
 dulational instability.\n\nPublications:\n\nR.M. Rozental\, A.V. Slunyaev\
 , N.S. Ginzburg\, A.S. Sergeev\, I.V. Zotova\, Self-similarity of rogue wa
 ve generation in gyrotrons: Beyond the Peregrine breather. Chaos\, Soliton
 s & Fractals 183\, 114884 (2024).\n\nA.V. Slunyaev\, Breathers of the nonl
 inear Schrödinger equation are coherent self-similar solutions. Physica D
  474\, 134575 (2025).\n\nC. Ward\, P. Kevrekidis\, Rogue waves as self-sim
 ilar solutions on a background: a direct calculation. Romanian J. Phys. 64
 \, 112 (2019).\n
LOCATION:https://researchseminars.org/talk/mmandim/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.V. Vedenyapin (Keldysh Institute of Applied Mathematics\, Russia
 n Academy of Sciences\, Moscow)
DTSTART:20260423T110000Z
DTEND:20260423T120000Z
DTSTAMP:20260422T225819Z
UID:mmandim/111
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/111/
 ">Cosmological solutions\, Hubble's law\, and accelerated expansion of the
  universe from the principle of least action</a>\nby V.V. Vedenyapin (Keld
 ysh Institute of Applied Mathematics\, Russian Academy of Sciences\, Mosco
 w) as part of Mathematical models and integration methods\n\n\nAbstract\nI
 n classic textbooks [1-3]\, the Hubble constant is defined in terms of the
  metric. Here\, we define it\, as expected\, in terms of matter\, followin
 g Milne and McCrea\, extending their theory of an expanding universe to th
 e relativistic case. This allows us to explain the accelerated expansion a
 s a simple relativistic effect\, without Einstein's lambda\, dark energy\,
  or new particles\, as an exact consequence of Einstein's classical action
 . The well-verified fact of accelerated expansion allows us to determine t
 he sign of the curvature in the Friedmann model: it turns out to be negati
 ve\, and we live in Lobachevsky space. Also in classical works (see [1–4
 ])\, equations for the fields are proposed without deriving the right-hand
  sides. Here we give a derivation of the right-hand sides of the Maxwell a
 nd Einstein equations within the framework of the Vlasov–Maxwell–Einst
 ein equations from the classical\, but slightly more general principle of 
 least action [5–6]. The resulting derivation of Vlasov-type equations yi
 elds Vlasov–Einstein equations that differ from those proposed previousl
 y. A method for transition from kinetic equations to hydrodynamic conseque
 nces is proposed [5–6]\, as was previously done by A.A. Vlasov himself [
 4]: this can be interpreted as a transition from a kinetic turbulent descr
 iption using a distribution function to a laminar description of the hydro
 dynamic type. This yields cosmological solutions of the Milne–McCrea typ
 e. In the case of Hamiltonian mechanics\, a transition from the hydrodynam
 ic consequences of the Liouville equation to the Hamilton-Jacobi equation 
 is possible\, as was already done in quantum mechanics by E. Madelung\, an
 d more generally by V.V. Kozlov [7] and V.P. Maslov. This yields Milne–M
 cCrea solutions in the nonrelativistic case\, as well as nonrelativistic a
 nd relativistic analyses of Friedmann-type solutions to the nonstationary 
 evolution of the Universe. This allows us to obtain the fact of the accele
 rated expansion of the Universe as a relativistic effect [8-10] without ar
 tificial additions such as Einstein's lambda\, dark energy\, and new field
 s\, from the classical relativistic principle of least action. This places
  general relativity and cosmology on a solid mathematical foundation and m
 akes it possible to explain the accelerated expansion\, a well-tested expe
 riment (with a Nobel Prize in 2011).\n\nReferences.\n\n1. Dubrovin\, B. A.
 \, Novikov\, S. P.\, and Fomenko\, A. T. “Modern Geometry: Methods and A
 pplications.” Moscow: Nauka\, 1986.\n\n2. Landau\, L. D.\, Lifshitz\, E.
  M. “Field Theory.” Moscow: Nauka\, 1988.\n\n3. Weinberg\, S. “Gravi
 tation and Cosmology.” Moscow: Mir\, 1975\, 696 p.\n\n4. Vlasov\, A. A. 
 “Statistical Distribution Functions.” Moscow: Nauka\, 1966\, 356 p.\n\
 n5. Vedenyapin\, V.\, Fimin\, N.\, Chechetkin\, V. “The generalized Frie
 dmann model as a self-similar solution of the Vlasov–Poisson equation sy
 stem.” European Physical Journal Plus. 2021. Vol. 136. No. 1. P. 71.\n\n
 6. V. V. Vedenyapin\, V. I. Parenkina\, S. R. Svirshchevskii\, “Derivati
 on of the Equations of Electrodynamics and Gravity from the Principle of L
 east Action”\, Comput. Math. Math. Phys.\, 62:6 (2022)\, 983–995.\n\n7
 . Kozlov V. V.\, General Theory of Vortices\, Udmurt University Press\, Iz
 hevsk\, 1998\, 239 p.\n\n8. V. V. Vedenyapin\, “Mathematical theory of t
 he expanding Universe based on the principle of least action”\, Russ. Co
 mput. Math. and Math. Phys.\, 64:11 (2024)\, 2114–2131\n\n9. V. V. Veden
 yapin\, Ya. G. Batishcheva\, M. V. Goryunova\, and A. A. Russkov\, “Math
 ematical theory of the accelerating expansion of the Universe based on the
  principle of least action”\, CMFD\, 71:4 (2025)\, 562–584.\n
LOCATION:https://researchseminars.org/talk/mmandim/111/
END:VEVENT
END:VCALENDAR