Soliton Dyanamics and Scattering

Avy Soffer, Mathematics Department, Rutgers University

A survey of results and problems of soliton dynamics in dispersive and hyperbolic nonlinear PDEs and the related spectral and scattering theory. I focus on the problem of large time behavior of the nonlinear Schrodinger equation, with both solitary and radiative waves appearing in the solution. The equations are nonintegrable in general and in arbitrary dimension. I will formulate the main conjectures relevant to soliton dynamics.