Multiple skew orthogonal polynomials and 2-component Pfaff lattice hierarchy

Autor:	Li, Shi-Hao, Shen, Bo-Jian, Xiang, Jie, Yu, Guo-Fu
Rok vydání:	2023
Předmět:	Mathematical Physics Nonlinear Sciences - Exactly Solvable and Integrable Systems
Druh dokumentu:	Working Paper
Popis:	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. Comment: 30 pages, comments are welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.02375 Zobrazit plný text záznamu View this record from Arxiv