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arXiv · 2603.29906

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

Jordan Berthoumieu
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Abstract

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.

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Jordan Berthoumieu. 2026-03-31. Construction of a multi-soliton-like solutions for non-integrable Schr\"odinger equations with non-trivial far field. https://arxiv.org/abs/2603.29906

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