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Matrix Orthogonal Polynomials, non-abelian Toda lattice and B\'acklund transformation
- Publication Year :
- 2021
-
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 B\"acklund 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.<br />Comment: 21 pages. Comments are welcome
- Subjects :
- Mathematical Physics
Nonlinear Sciences - Exactly Solvable and Integrable Systems
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2109.00671
- Document Type :
- Working Paper