Nonlinear waves in dispersive partial differential equations
Speaker: Sylvie Benzoni-Gavage (Institute Camille Jordan, Lyon 1 University)

Time: 9h30, Tuesday, April 25, 2017
Location: Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: 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.