BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:A.M. Kamchatnov (Institute of Spectroscopy Russian Academy of Scie nces\, Moscow\, Russia) DTSTART:20251204T110000Z DTEND:20251204T120000Z DTSTAMP:20260423T005851Z UID:mmandim/102 DESCRIPTION:Title: Asymptotic integrability of nonlinear wave equations\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 END:VCALENDAR