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<p>This paper develops the Cauchy matrix approach to formulate the non-isospectral Korteweg-de Vries equation and derive its explicit soliton solutions. A Sylvester equation is employed to define a set of scalar functions <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\{ S^{(i,j)}\}\)</EquationSource> </InlineEquation>. By introducing non- isospectral dispersion relations, the evolution equations for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\{ S^{(i,j)}\}\)</EquationSource> </InlineEquation> are systematically established. Several fundamental identities of these functions are utilized to verify the correctness of the obtained solutions. Moreover, explicit soliton solutions are presented, accompanied by a detailed analysis of their dynamical characteristics.</p>

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Non-Isospectral Korteweg-de Vries Equation from the Cauchy Matrix Approach

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  • 出版模式：

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  • 发表日期：

    2026年2月6日

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  • Alemu Yilma Tefera,
  • Solomon Bekele Zegeye

摘要

This paper develops the Cauchy matrix approach to formulate the non-isospectral Korteweg-de Vries equation and derive its explicit soliton solutions. A Sylvester equation is employed to define a set of scalar functions \(\{ S^{(i,j)}\}\) . By introducing non- isospectral dispersion relations, the evolution equations for \(\{ S^{(i,j)}\}\) are systematically established. Several fundamental identities of these functions are utilized to verify the correctness of the obtained solutions. Moreover, explicit soliton solutions are presented, accompanied by a detailed analysis of their dynamical characteristics.