Matrix orthogonal polynomials,non-abelian Toda lattices,and B?cklund transformations

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外文摘要：A connection between matrix orthogonal polynomials and non-abelian integrable lattices is investigated in this paper.The normalization factors of matrix orthogonal polynomials expressed using quasi-determinants are shown to be the solutions to the non-abelian Toda lattice in semi-discrete and full-discrete cases.Moreover,with a moment modification method,we demonstrate that the Bäcklund transformation of the non-abelian Toda lattice given by Popowicz(1983)is equivalent to the non-abelian Volterra lattice,whose solutions can be expressed using quasi-determinants as well.

外文关键词：

matrix orthogonal polynomialnon-abelian Toda latticeBäcklund transformationquasi-determinant technique

作者：

Shi-Hao Li

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作者单位：

Department of Mathematics,Sichuan University,Chengdu 610064,China

基金：

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of China

项目编号：

121014321217515511971322

出版年：

2024

DOI：

10.1007/s11425-022-2168-x

中国科学:数学(英文版)

中国科学院

中国科学:数学(英文版)

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影响因子：0.36

ISSN：1674-7283

年,卷(期)：2024.67(9)