Solutions to the SU($\mathcal{N}$) self-dual Yang-Mills equation

Autor:	Li, Shangshuai, Qu, Changzheng, Zhang, Da-jun
Rok vydání:	2022
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems
Druh dokumentu:	Working Paper
DOI:	10.1016/j.physd.2023.133828
Popis:	In this paper we aim to derive solutions for the SU($\mathcal{N}$) self-dual Yang-Mills (SDYM) equation with arbitrary $\mathcal{N}$. A set of noncommutative relations are introduced to construct a matrix equation that can be reduced to the SDYM equation. It is shown that these relations can be generated from two different Sylvester equations, which correspond to the two Cauchy matrix schemes for the (matrix) Kadomtsev-Petviashvili hierarchy and the (matrix) Ablowitz-Kaup-Newell-Segur hierarchy, respectively. In each Cauchy matrix scheme we investigate the possible reductions that can lead to the SU$(\mathcal{N})$ SDYM equation and also analyze the physical significance of some solutions, i.e. being Hermitian, positive-definite and of determinant being one. Comment: 26 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.08574 Zobrazit plný text záznamu View this record from Arxiv