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.
基金
supported by National Natural Science Foundation of China(Grant Nos.12101432,12175155,and 11971322)。
