From the self-dual Yang-Mills equation to the Fokas-Lenells equation

Autor:	Li, Shangshuai, Liu, Shuzhi, Zhang, Da-jun
Rok vydání:	2024
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	A reduction from the self-dual Yang-Mills (SDYM) equation to the unreduced Fokas-Lenells (FL) system is described in this paper. It has been known that the SDYM equation can be formulated from the Cauchy matrix schemes of the matrix Kadomtsev-Petviashvili (KP) hierarchy and the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy. We show that the reduction can be realized in these two Cauchy matrix schemes, respectively. Each scheme allows us to construct solutions for the unreduced FL system. We prove that these solutions obtained from different schemes are equivalent under certain reflection transformation of coordinates. Using conjugate reduction we obtain solutions of the FL equation. The paper adds an important example to Ward's conjecture on the reductions of the SDYM equation. It also indicates the Cauchy matrix structures of the Kaup-Newell hierarchy. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.10807 Zobrazit plný text záznamu View this record from Arxiv