On asymptotic stability of ground states of NLS with a finite bands periodic potential in 1D

TL;DR

This paper proves the asymptotic stability of ground states in a 1D nonlinear Schrödinger equation with a finite bands periodic potential, assuming orbital stability.

Contribution

It establishes the asymptotic stability of ground states under certain hypotheses for the first time in this setting.

Findings

Ground states are asymptotically stable under specified conditions.

The stability analysis applies to finite bands periodic potentials in 1D.

The work extends understanding of stability in nonlinear Schrödinger equations.

Abstract

We consider a nonlinear Schroedinger equation with a finite bands periodic potential in R . We assume the existence of an orbitally stable family of ground states. We prove that under appropriate hypotheses the ground states are asymptotically stable.