Multiple skew orthogonal polynomials and 2-component Pfaff lattice hierarchy
Mathematical Physics
2023-02-07 v1 math.MP
Exactly Solvable and Integrable Systems
Abstract
In this paper, we introduce multiple skew-orthogonal polynomials and investigate their connections with classical integrable systems. By using Pfaffian techniques, we show that multiple skew-orthogonal polynomials can be expressed by multi-component Pfaffian tau-functions upon appropriate deformations. Moreover, a two-component Pfaff lattice hierarchy, which is equivalent to the Pfaff-Toda hierarchy studied by Takasaki, is obtained by considering the recurrence relations and Cauchy transforms of multiple skew-orthogonal polynomials.
Cite
@article{arxiv.2302.02375,
title = {Multiple skew orthogonal polynomials and 2-component Pfaff lattice hierarchy},
author = {Shi-Hao Li and Bo-Jian Shen and Jie Xiang and Guo-Fu Yu},
journal= {arXiv preprint arXiv:2302.02375},
year = {2023}
}
Comments
30 pages, comments are welcome!