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<p>This paper establishes a Cauchy matrix scheme for the BKP equation based on a specific Sylvester equation and corresponding master functions. Within this framework, we systematically derive the BKP equation together with its <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\tau \)</EquationSource> </InlineEquation>-function and Lax pair. Through dimensional reductions, the BKP system is reduced to the SK and bSK equations, and their exact solutions are obtained. Furthermore, starting from a soliton solution of the BKP equation, we construct both singular solutions that exhibit isolated blow-up points and regular (non-singular) solutions. Graphical illustrations of these singular and regular solutions are provided.</p>

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Cauchy Matrix Structure Underlying the BKP Equation and its Dimensional Reductions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月4日

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  • Ying-ying Sun,
  • Xin Shen,
  • Shi-han Zhang

摘要

This paper establishes a Cauchy matrix scheme for the BKP equation based on a specific Sylvester equation and corresponding master functions. Within this framework, we systematically derive the BKP equation together with its \(\tau \) -function and Lax pair. Through dimensional reductions, the BKP system is reduced to the SK and bSK equations, and their exact solutions are obtained. Furthermore, starting from a soliton solution of the BKP equation, we construct both singular solutions that exhibit isolated blow-up points and regular (non-singular) solutions. Graphical illustrations of these singular and regular solutions are provided.