Nonlinear Modulational Instability of Dispersive PDE Models

题目: Nonlinear Modulational Instability of Dispersive PDE Models

报告人: 林治武 教授     佐治亚理工学院

报告时间: 2017.12.20 星期三  15:00-16:00

报告地点: 知新楼B1032报告厅

摘要: We prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations (e.g. the Whitham equation, the generalized KDV equation, the Benjamin-Ono equation), the nonlinear

Schrödinger equation and the BBM equation. First, the semigroup estimates required for the nonlinear proof are obtained by using the Hamiltonian structures of the linearized PDEs; Second, for KDV type equations the loss of derivative in the nonlinear term is overcome in two complementary cases by constructing higher order approximation solutions or by a bootstrap argument. This is joint work with Jiayin Jin and Shasha Liao.