Soliton dynamics in a potential


Robert Jerrard

University of Illinois at Urbana-Champaign


I will discuss a theorem that characterizes the behavior of solutions of focussing nonlinear Schr\"odinger equation with a potential, for initial data that looks like a point particle. The theorem proves that, in the semiclassical limit, this particle persists and evolves via the classical Newtonian trajectory. This resolves a conjecture of A. Weinstein that dates from about 1980.

INSCC 110, 3:30pm Monday, April 26, 1999