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

Shi-Hao Li

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arXiv · 2109.00671

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

Shi-Hao Li

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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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Shi-Hao Li. 2021-09-28. Matrix Orthogonal Polynomials, non-abelian Toda lattice and Bäcklund transformation. https://arxiv.org/abs/2109.00671

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