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<p>We study the existence of periodic peaked traveling wave solution for a generalized modified <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2025_289_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mu \)</EquationSource> </InlineEquation>-Camassa-Holm equation closely related to the modified <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2025_289_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mu \)</EquationSource> </InlineEquation>-Camassa-Holm equation [<CitationRef CitationID="CR26">26</CitationRef>] with cubic nonlinearity and the generalized modified Camassa-Holm equation [<CitationRef CitationID="CR2">2</CitationRef>] with higher nonlinearity. We prove that the equation admits the periodic peaked traveling wave solutions.</p>

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Periodic Peaked Traveling Wave Solution for a Generalized Modified \(\mu \)-Camassa-Holm Equation

  • 期刊论文

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  • 发表日期：

    2025年6月3日

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  • Byungsoo Moon

摘要

We study the existence of periodic peaked traveling wave solution for a generalized modified \(\mu \) -Camassa-Holm equation closely related to the modified \(\mu \) -Camassa-Holm equation [26] with cubic nonlinearity and the generalized modified Camassa-Holm equation [2] with higher nonlinearity. We prove that the equation admits the periodic peaked traveling wave solutions.