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

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.