Non-existence of internal mode for small solitary waves of the 1D Zakharov system

2025/11/02 by Martel, Yvan, Rialland, Guillaume
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.01116

Abstract

We prove that the linearised operator around any sufficiently small solitary wave of the one-dimensional Zakharov system has no internal mode. This spectral result, along with its proof, is expected to play a role in the study of the asymptotic stability of solitary waves.

Citations

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Related

• Asymptotic stability of solitary waves for the 1D near-cubic non-linear Schrödinger equation in the absence of internal modes
• Multi-solitary waves for the one-dimensional Zakharov system
• Asymptotic stability of a finite sum of solitary waves for the Zakharov-Kuznetsov equation
• Asymptotic stability of solitons for near-cubic NLS equation with an internal mode
• Stability for line solitary waves of Zakharov-Kuznetsov equation