Solutions to the SU(N) self-dual Yang-Mills equation

被引：5
|
作者：
Li, Shangshuai [1 ]
Qu, Changzheng [2 ]
Zhang, Da-jun [1 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
[2] Ningbo Univ, Sch Math & Stat, Ningbo 315211, Peoples R China
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2023年 / 453卷
基金：
中国国家自然科学基金;
关键词：
Self-dual Yang-Mills equation; Cauchy matrix approach; Sylvester equation; Exact solution; Integrable system; SYLVESTER EQUATION; INTEGRABLE EQUATIONS; MODEL;
D O I：
10.1016/j.physd.2023.133828
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we aim to derive solutions for the SU(N) self-dual Yang-Mills (SDYM) equation with arbitrary 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(N) SDYM equation and also analyze the physical significance of some solutions, i.e. being Hermitian, positive-definite and of determinant being one.& COPY; 2023 Elsevier B.V. All rights reserved.
引用
收藏
页数：17
相关论文
共 50 条
12345