Soliton dynamics of nonlinear dispersive PDE

For several nonlinear dispersive PDE's, the solutions behave like the sum of solitons and dispersive wave. The interaction between them determines the properties of the solutions. This study is also related to that of blow-up solutions. In this talk we will examine generalized KdV and Schrodinger equations. In particular, we show that an excited state of a Schrodinger equation is like a hyperbolic periodic orbit in dynamical systems with stable/unstable manifolds.