Scholarlink

Abstract <p> Cauchy matrix approach is developed to construct the nonisospectral and variable-coefficient equations and study their integrability. We derive the nonisospectral and variable-coefficient Kadomtsev–Petviashvili ( n-vcKP) equation, which includes the standard KP equation and the nonisospectral and variable-coefficient KdV equation as special cases. The connection of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2605_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau\)</EquationSource> </InlineEquation> function of the n-vcKP equation with the Cauchy matrix approach is clarified. The Lax pair for the n-vcKP equation is derived in a systematic way. Two types of exact solutions are found by solving the corresponding Sylvester equation. </p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Cauchy matrix approach to the nonisospectral and variable-coefficient Kadomtsev–Petviashvili equation

  • 期刊论文

  • 发表日期：

    2025年3月25日

查看全文
  • Zhen Zhou,
  • Xinyuan Zhang,
  • Tong Shen,
  • Chunxia Li

摘要

Abstract

Cauchy matrix approach is developed to construct the nonisospectral and variable-coefficient equations and study their integrability. We derive the nonisospectral and variable-coefficient Kadomtsev–Petviashvili ( n-vcKP) equation, which includes the standard KP equation and the nonisospectral and variable-coefficient KdV equation as special cases. The connection of the \(\tau\) function of the n-vcKP equation with the Cauchy matrix approach is clarified. The Lax pair for the n-vcKP equation is derived in a systematic way. Two types of exact solutions are found by solving the corresponding Sylvester equation.