On Soliton Dynamics in Nonlinear Schrodinger Equations

TL;DR

This paper studies the long-term behavior of solitons in nonlinear Schrödinger equations with external potentials, showing how solutions decompose into a localized soliton and a dispersing term under certain conditions.

Contribution

It provides a rigorous analysis of the asymptotic dynamics of solitons in the presence of external potentials, establishing conditions for their stability and decomposition.

Findings

Solitons form around local minima of the potential.

Solutions decompose into a soliton and a dispersing component.

Conditions on nonlinearity and initial data ensure this decomposition.

Abstract

In this paper we announce the result of asymptotic dynamics of solitons of nonlinear Schrodinger equations with external potentials. To each local minima of the potential there is a soliton centered around it. Under some conditions on the nonlinearity, the potential and the datum, we prove that the solution can be decomposed into two parts: the soliton and the term dissipating to infinity.