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arXiv · 2510.27402

Nonisospectral deformations of noncommutative Laurent biorthogonal polynomials and matrix discrete Painlev\'e-type equations

Dan Dai·Xiaolu Yue
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Abstract

In this paper, we establishes a connection between noncommutative Laurent biorthogonal polynomials (bi-OPs) and matrix discrete Painlev\'e (dP) equations. We first apply nonisospectral deformations to noncommutative Laurent bi-OPs to obtain the noncommutative nonisospectral mixed relativistic Toda lattice and its Lax pair. Then, we perform a stationary reduction on this Lax pair to obtain a matrix dP-type equation. The validity of this reduction is demonstrated through a specific choice of weight function and the application of quasideterminant properties. In the scalar case, our matrix dP equation reduces to the known alternate dP II equation.

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Dan Dai, Xiaolu Yue. 2025-10-31. Nonisospectral deformations of noncommutative Laurent biorthogonal polynomials and matrix discrete Painlev\'e-type equations. https://arxiv.org/abs/2510.27402

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