Nonisospectral deformations of noncommutative Laurent biorthogonal polynomials and matrix discrete Painlev\'e-type equations
Exactly Solvable and Integrable Systems
2026-05-29 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2510.27402,
title = {Nonisospectral deformations of noncommutative Laurent biorthogonal polynomials and matrix discrete Painlev\'e-type equations},
author = {Dan Dai and Xiaolu Yue},
journal= {arXiv preprint arXiv:2510.27402},
year = {2026}
}
Comments
15 pages