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<p>This paper intends to construct discrete spectral transformations for Cauchy–Jacobi orthogonal polynomials and to find its corresponding discrete integrable systems. It turns out that the normalization factor of Cauchy–Jacobi orthogonal polynomials acts as the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>-function of the discrete CKP equation, which has been applied into Yang–Baxter equation, integrable geometry, cluster algebra, and so on.</p>

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Cauchy–Jacobi orthogonal polynomials and the discrete CKP equation

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Shi-Hao Li,
  • Satoshi Tsujimoto,
  • Ryoto Watanabe,
  • Guo-Fu Yu

摘要

This paper intends to construct discrete spectral transformations for Cauchy–Jacobi orthogonal polynomials and to find its corresponding discrete integrable systems. It turns out that the normalization factor of Cauchy–Jacobi orthogonal polynomials acts as the \(\tau \) τ -function of the discrete CKP equation, which has been applied into Yang–Baxter equation, integrable geometry, cluster algebra, and so on.