Scholarlink

<p>We present the first explicit derivation of a matrix Painlevé IV equation arising from semi-classical matrix orthogonal polynomials of Laguerre-type. Starting from the discrete nonlinear relations for the recurrence coefficients of the associated matrix orthogonal polynomials, established in [<CitationRef CitationID="CR9">9</CitationRef>] and identified there as a discrete Painlevé&#xa0;IV equation, we show that the recurrence coefficients satisfy a nonlinear matrix differential-difference equation in the deformation parameter <i>t</i>. These continuous equations provide a natural matrix analogue of the classical Painlevé IV equation, reducing to the scalar case when all coefficients commute. We conclude with a new concrete asymmetric low-dimensional example illustrating the main result.</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

Matrix semi-classical Laguerre orthogonal polynomials and non-commutative non-linear equations

  • 期刊论文

  • 发表日期：

    2026年8月5日

查看全文
  • Assil Fradi

摘要

We present the first explicit derivation of a matrix Painlevé IV equation arising from semi-classical matrix orthogonal polynomials of Laguerre-type. Starting from the discrete nonlinear relations for the recurrence coefficients of the associated matrix orthogonal polynomials, established in [9] and identified there as a discrete Painlevé IV equation, we show that the recurrence coefficients satisfy a nonlinear matrix differential-difference equation in the deformation parameter t. These continuous equations provide a natural matrix analogue of the classical Painlevé IV equation, reducing to the scalar case when all coefficients commute. We conclude with a new concrete asymmetric low-dimensional example illustrating the main result.