Orbital stability of a chain of dark solitons for general nonintegrable Schr\"odinger equations with non-zero condition at infinity

TL;DR

This paper proves the orbital stability of a chain of dark solitons in a general 1D nonlinear Schrödinger equation with non-zero boundary conditions, extending stability results to nonintegrable cases.

Contribution

It establishes the orbital stability of a chain of traveling dark solitons near the speed of sound in a nonintegrable Schrödinger equation, using advanced analytical techniques.

Findings

Proved orbital stability of dark soliton chains

Extended stability results to nonintegrable equations

Applied and adapted existing analytical methods

Abstract

In this article, we focus on the stability of dark solitons for a general one-dimensional nonlinear Schr\"odinger equation. More precisely, we prove the orbital stability of a chain of travelling waves whose speeds are well ordered, taken close to the speed of sound c s and such that the solitons are initially localized far away from each other. The proof relies on the arguments developed by F. B\'ethuel, P. Gravejat and D. Smets and first introduced by Y. Martel, F. Merle and T.-P. Tsai.