The Nonlinear Schroedinger equation: solitons dynamics

Abstract

In this paper we investigate the dynamics of solitons occurring in the nonlinear Schroedinger equation when a parameter h->0. We prove that under suitable assumptions, the the soliton approximately follows the dynamics of a point particle, namely, the motion of its barycenter $q_h(t)$ satisfies the equation $ddot{q}_h(t)+\nabla V(q_h(t))=H_h(t)$ where $\sup_{t\in R} |H_h(t)| -> 0$ as h->0.