Title: Cauchy matrix approach and its application in anti-self-dual Yang-Mills equation

Abstract:
In this talk, I will introduce the Cauchy matrix approach, a powerful direct algebraic method, as an effective tool for investigating nonlinear equations in integrable systems. The Cauchy matrix approach starts from a Sylvester equation and dispersion relations, from which a master function $S^{(i,j)}$ is determined. The derivatives of $S^{(i,j)}$, along with certain properties of this function, are then used to construct several integrable equations and derive their N-soliton solutions.
Recently, our research team has applied this method to solve the SU(N) anti-self-dual Yang-Mills equation. The relevant work has been updated on arXiv: https://arxiv.org/pdf/2211.08574. This is a joint work with Da-jun Zhang and Chang-zheng Qu.

Reporter: Shangshuai Li 李上帥
Affiliation: Shanghai University 上海大学 & Waseda University 早稲田大学