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arXiv · 2511.01116

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

Yvan Martel·Guillaume Rialland
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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.

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Yvan Martel, Guillaume Rialland. 2025-11-02. Non-existence of internal mode for small solitary waves of the 1D Zakharov system. https://arxiv.org/abs/2511.01116

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