- \n
- the method of the differential separability conditions\; \n
- the method of the vecto r fields $Z$. \n

\n< a href="https://arxiv.org/abs/1007.3543">arXiv:1007.3543

\nhttps://dx.doi.org/10. 1080/14029251.2017.1418057

\narXiv:1608.03994

\narXiv:2101.04523\, Mi tm f10046

\narXiv:2203.070 62

\narXiv:2212.07583\n LOCATION:https://researchseminars.org/talk/GDEq/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Georgy Sharygin DTSTART;VALUE=DATE-TIME:20221221T162000Z DTEND;VALUE=DATE-TIME:20221221T180000Z DTSTAMP;VALUE=DATE-TIME:20230921T154957Z UID:GDEq/76 DESCRIPTION:Title: Ch opping integrals of the full symmetric Toda system\, a new approach\nb y Georgy Sharygin as part of Geometry of differential equations seminar\n\ nLecture held in room 303 of the Independent University of Moscow.\n\nAbst ract\nIn my talk I will try to answer the questions that has been causing my anxiety for a rather long time: where do the additional integrals of th e full symmetric Toda system come from\, why they are rational and what do es all this have to do with "chopping". Even if we can use the AKS method there remains the question\, why do the initial functions actually commute (and whether it is possible to find other with the same property). The kn own answers were concerned either with rather hard straightforward computa tions\, or with the properties of a Gaudin system\; they look pretty compl icated. In my talk I will show how one can obtain these integrals with the help of some simple differential operators (in the manner of the argument shift method). Besides this\, we will discuss some other possible integra ls as well as the method to solve the corresponding flows by QR decomposit ion.\n\nThe talk is based on a common work with Yu. Chernyakov and D. Tala laev.\n LOCATION:https://researchseminars.org/talk/GDEq/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Lychagin DTSTART;VALUE=DATE-TIME:20221207T162000Z DTEND;VALUE=DATE-TIME:20221207T180000Z DTSTAMP;VALUE=DATE-TIME:20230921T154957Z UID:GDEq/77 DESCRIPTION:Title: On normal forms of differential operators\nby Valentin Lychagin as part of Geometry of differential equations seminar\n\nLecture held in room 303 of the Independent University of Moscow.\n\nAbstract\nIn this talk\, we cl assify linear (as well as some special nonlinear) scalar diff\nerential op erators of order $k$ on $n$-dimensional manifolds with respect to the diff eomorphism pseudogroup.\n Cases\, when $k = 2$\, $\\forall n$\, and $ k = 3$\, $n = 2$\, were discussed before\, and now we consider cases $k\\g e5$\, $n = 2$ and $k\\ge4$\, $n = 3$ and $k\\ge3$\, $n\\ge4$. In all these cases\, the fields of rational differential invariants are generated by t he 0-order invariants of symbols.\n\nThus\, at first\, we consider the cla ssical problem of Gl-invariants of $n$-ary forms. We'll illustrate here th e power of the differential algebra approach to this problem and show how to find the rational Gl-invariants of $n$-are forms in a constructive way. \n\nAfter all\, we apply the $n$ invariants principle in order to get (loc al as well as global) normal forms of linear operators with respect to the diffeomorphism pseudogroup.\n\nDepending on available time\, we show how to extend all these results to some classes of nonlinear operators.\n LOCATION:https://researchseminars.org/talk/GDEq/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergey Tsarev\, Folkert Müller-Hoissen\, Dmitry Millionschikov\, Boris Konopelchenko DTSTART;VALUE=DATE-TIME:20221214T140000Z DTEND;VALUE=DATE-TIME:20221214T180000Z DTSTAMP;VALUE=DATE-TIME:20230921T154957Z UID:GDEq/78 DESCRIPTION:Title: On e day workshop in honor of Maxim Pavlov's 60th birthday\nby Sergey Tsa rev\, Folkert Müller-Hoissen\, Dmitry Millionschikov\, Boris Konopelchenk o as part of Geometry of differential equations seminar\n\nLecture held in room 303 of the Independent University of Moscow.\n\nAbstract\n

\n\n

- \n
- Integrable systems of Jordan block typ e and modified KP hierarchy\; \n
- Hamiltonian aspects of quasilinear systems of Jordan block type\; \n
- Example: delta-functional reduct ions of the soliton gas equation. \n