BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:S.P. Tsarev (Siberian Federal University\, Krasnoyarsk) DTSTART:20220331T110000Z DTEND:20220331T120000Z DTSTAMP:20260423T005823Z UID:mmandim/38 DESCRIPTION:Title: Generalized factorization of second-order linear partial differential ope rators and reflectionless wave propagation in shallow water\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 END:VCALENDAR