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<p>This paper considers the orbital stability of <i>N</i>-smooth solitary waves for the cubic Camassa-Holm-type equation, derived from the shallow water theory. We demonstrate that the train of <i>N</i>-smooth solitary waves, subjected to a small perturbation, retains its orbital stability in the energy space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="28_2025_1085_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^{1}({\mathbb {R}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>H</mi> <mn>1</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> based on three key properties: the modulation arguments, the almost monotonicity of functionals, and the local coercivity of the solitary wave solution.</p>

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Orbital stability of the trains of smooth solitary waves for the cubic Camassa-Holm-type equation

  • 期刊论文

  • 发表日期：

    2025年5月24日

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  • XiaoQing Sun,
  • Ting Luo

摘要

This paper considers the orbital stability of N-smooth solitary waves for the cubic Camassa-Holm-type equation, derived from the shallow water theory. We demonstrate that the train of N-smooth solitary waves, subjected to a small perturbation, retains its orbital stability in the energy space \(H^{1}({\mathbb {R}})\) H 1 ( R ) based on three key properties: the modulation arguments, the almost monotonicity of functionals, and the local coercivity of the solitary wave solution.