BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org 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:20260423T005804Z UID:mmandim/108 DESCRIPTION:Title: Solutions to the nonlinear Schrodinger equation with an anti-Hermitian t erm\, localized on curves\, and quasi steady vortex states\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 END:VCALENDAR