arXiv subjects

Jordan Berthoumieu

Publications and source records attributed to Jordan Berthoumieu.

4 recordsLinked to original sources

arXiv2026

Construction of a multi-soliton-like solutions for non-integrable Schr\"odinger equations with non-trivial far field

This article provides a naturel sequel of previous works [6, 4] regarding the stability of travelling waves for a general one-dimensional Schr\"odinger equation (N LS) with non-zero condition at infinity. The aim of this article is twofold. First, we prove the asymptotic stability of well-prepared chains of dark solitons and secondly, we construct an asymptotic N -soliton-like solution, which is an exact solution of (N LS), the large-time dynamics of which is similar to a decoupled chain of solitons.

math.AP↗

arXiv2026

Asymptotic stability of travelling waves for general nonlinear Schrödinger equations with non-zero condition at infinity

In previous works [4, 5], existence and uniqueness of travelling waves for the nonlinear Schrödinger equations have been shown for speeds close to the speed of sound. Furthermore, it has been proved that a chain of dark solitons of well-ordered speeds near the sound speed, taken initially apart from each other, is orbitally stable. In this article, we complete this study by proving the asymptotic stability of these travelling waves, namely that a solution initially close to a travelling wave eventually converges towards a travelling wave of close speed. This relies on the methods used by F. Béthuel, P. Gravejat and D. Smets in [6] and first introduced by Y. Martel and F. Merle in [22].

math.AP↗

arXiv2024

Orbital stability of a chain of dark solitons for general nonintegrable Schrödinger equations with non-zero condition at infinity

In this article, we focus on the stability of dark solitons for a general one-dimensional nonlinear Schrödinger 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. Béthuel, P. Gravejat and D. Smets and first introduced by Y. Martel, F. Merle and T.-P. Tsai.

math.AP↗

arXiv2024

Minimizing travelling waves for the one-dimensional nonlinear Schrödinger equation with non-zero condition at infinity

This paper deals with the existence of travelling wave solutions for a general one-dimensional nonlinear Schrödinger equation. We construct these solutions by minimizing the energy under the constraint of fixed momentum. We also prove that the family of minimizers is stable. Our method is based on recent articles about the orbital stability for the classical and non-local Gross-Pitaevskii equations [3, 10]. It relies on a concentration-compactness theorem, which provides some compactness for the minimizing sequences and thus the convergence (up to a subsequence) towards a travelling wave solution.

math.AP↗