Người báo cáo: Sylvie Benzoni-Gavage (Institute Camille Jordan, Lyon 1 University)
Thời gian: 9h30, Thứ 3 ngày 25/4/2017
Địa điểm: Phòng 4, Nhà A14, Viện Toán học, 18 Hoàng Quốc Việt, Cầu Giấy, Hà Nội
Tóm tắt: Many nonlinear partial differential equations (PDEs) of dispersive type are endowed with a Hamiltonian structure, and admit rich families of planar traveling waves that are periodic in both time and space - the limiting case of an infinite period corresponding to solitary waves. The talk will concentrate on a class of dispersive PDEs that is ubiquitous in mathematical physics, which includes the NonLinear Schrödinger equation, generalized Korteweg-de Vries equations, and dispersive perturbations of the Euler equations for compressible fluids. The main purpose is to establish stability criteria for periodic traveling waves, and make the connection with the stability theory of solitary waves, which was initiated by Boussinesq 140 years ago and awaited more than century to be made rigorous. |
