Asymptotic stability of solitary waves for the 1D near-cubic non-linear Schrödinger equation in the absence of internal modes - Université de Versailles Saint-Quentin-en-Yvelines Access content directly
Journal Articles Nonlinear Analysis: Theory, Methods and Applications Year : 2024

Asymptotic stability of solitary waves for the 1D near-cubic non-linear Schrödinger equation in the absence of internal modes

Abstract

We consider perturbations of the one-dimensional cubic Schrödinger equation, under the form . Under hypotheses on the function that can be easily verified in some cases, we show that the linearized problem around a solitary wave does not have internal mode (nor resonance) and we prove the asymptotic stability of these solitary waves, for small frequencies.

Dates and versions

hal-04439096 , version 1 (05-02-2024)

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Guillaume Rialland. Asymptotic stability of solitary waves for the 1D near-cubic non-linear Schrödinger equation in the absence of internal modes. Nonlinear Analysis: Theory, Methods and Applications, 2024, 241, pp.113474. ⟨10.1016/j.na.2023.113474⟩. ⟨hal-04439096⟩
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