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arXiv 2407.08486nlin.SI
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非交换非等谱Toda与Lotka-Volterra格，以及矩阵离散Painlevé方程

Noncommutative nonisospectral Toda and Lotka-Volterra lattices, and matrix discrete Painlevé equations

Anhui Yan, Chunxia Li

备注：
After we posted our paper arXiv:submit/5730163 on arXiv, we got an email from Xiaolu Yue. She told us that they also worked on this topic and sent us their results. Since we have achieved the results at the same time individually, we decided to collaborate after discussion. We'd like to withdraw this paper if possible and submit it after revision. I'm sorry for the inconvenience. Thank you
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AI总结：

本文提出非交换非等谱Toda与Lotka-Volterra格，通过非等谱变形导出矩阵离散Painlevé I方程，并给出拟行列式解以证明平稳约化的合理性。

摘要：

通过对无特定权函数的矩阵正交多项式和矩阵对称正交多项式进行非等谱变形，提出并研究了非等谱Toda和Lotka-Volterra格的非交换类似物。在平稳约化下，不仅从非交换非等谱格本身，而且从它们的Lax对中，分别导出了矩阵离散Painlevé I方程和矩阵非对称离散Painlevé I方程。平稳约化的合理性已在为相应矩阵离散Painlevé方程提供拟行列式解的意义上得到证明。

英文摘要：

The noncommutative analogues of the nonisospectral Toda and Lotka-Volterra lattices are proposed and studied by performing nonisopectral deformations on the matrix orthogonal polynomials and matrix symmetric orthogonal polynomials without specific weight functions, respectively. Under stationary reductions, matrix discrete Painlevé I and matrix asymmetric discrete Painlevé I equations are derived separately not only from the noncommutative nonisospectral lattices themselves, but also from their Lax pairs. The rationality of the stationary reduction has been justified in the sense that quasideterminant solutions are provided for the corresponding matrix discrete Painlevé equations.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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