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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月23日

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  • Yvan Martel,
  • Guillaume Rialland

摘要

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.