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

作     者：Shi-Hao Li 

作者机构：Department of Mathematics Sichuan University 

出 版 物：《Science China Mathematics》 (中国科学:数学(英文版))

年 卷 期：2024年第67卷第9期

页      面：2071-2090页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 12101432  12175155  and 11971322) 

主　　题：matrix orthogonal polynomial non-abelian Toda lattice Bäcklund transformation quasi-determinant technique 

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 quasideterminants 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 B¨acklund 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.