Matrix Orthogonal Polynomials, non-abelian Toda lattice and Bäcklund transformation

2021/09/02 by Li, Shi-Hao · 3 citations
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2109.00671

Abstract

A connection between matrix orthogonal polynomials and non-abelian integrable lattices is investigated in this paper. The normalization factors of matrix orthogonal polynomials expressed by quasi-determinant are shown to be solutions of non-abelian Toda lattice in semi-discrete and full-discrete cases. Moreover, with a moment modification method, we demonstrate that the Bäcklund transformation of non-abelian Toda given by Popowicz is equivalent to the non-abelian Volterra lattice, whose solutions could be expressed by quasi-determinants as well.

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• Quasi-Pfaffians and applications
• Nonisospectral deformations of noncommutative Laurent biorthogonal polynomials and matrix discrete Painlevé-type equations
• Non-commutative multiple bi-orthogonal polynomials: formal approach and integrability

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