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Abstract <p> We study periodic solutions of the generalized Camassa–Holm equation (CH-<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2620_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma\)</EquationSource> </InlineEquation> equation). We show that the generalized CH-<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2620_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma\)</EquationSource> </InlineEquation> equation is also an important theoretical model because it is a completely integrable system. We obtain representation for periodic solutions of the generalized CH-<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2620_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma\)</EquationSource> </InlineEquation> equation in the framework of the inverse spectral problem for a weighted Sturm–Liouville operator. </p>

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Integration of the generalized Camassa–Holm equation in the class of periodic functions

  • 期刊论文

  • 发表日期：

    2025年4月25日

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  • B. A. Babajanov,
  • D. O. Atajonov

摘要

Abstract

We study periodic solutions of the generalized Camassa–Holm equation (CH- \(\gamma\) equation). We show that the generalized CH- \(\gamma\) equation is also an important theoretical model because it is a completely integrable system. We obtain representation for periodic solutions of the generalized CH- \(\gamma\) equation in the framework of the inverse spectral problem for a weighted Sturm–Liouville operator.