Back to Search
Start Over
Matrix-valued $\theta$-deformed bi-orthogonal polynomials, Non-commutative Toda theory and B\'acklund transformation
- Publication Year :
- 2023
-
Abstract
- This paper is devoted to revealing the relationship between matrix-valued $\theta$-deformed bi-orthogonal polynomials and non-commutative Toda-type hierarchies. In this procedure, Wronski quasi-determinants are widely used and play the role of non-commutative $\tau$-functions. At the same time, B\"acklund transformations are realized by using a moment modification method and non-commutative $\theta$-deformed Volterra hierarchies are obtained, which contain the known examples of the Itoh-Narita-Bogoyavlensky lattices and the fractional Volterra hierarchy.<br />Comment: 30 pages. Comments are welcome
- Subjects :
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2305.17962
- Document Type :
- Working Paper