一类可积非局部CLL方程的求解
Solution to a Class of Integrable Nonlocal CLL Equations
摘要: 本文基于耦合的Chen-Lee-Liu方程，通过约化得到一类可积非局部的CLL方程，并由可积非局部CLL方程Lax对出发，构造了双边Darboux变换，从而得到零背景下解的表达式。经典的Chen-Lee-Liu (CLL)方程是数学和物理中最重要的可积系统之一，可用于描述光纤中的传播脉冲。目前已经通过Darboux变换法、黎曼–希尔伯特方法、逆散射方法等方法对CLL方程进行求解，得到许多有趣的解。本文从经典耦合的CLL方程扩展到非局部的CLL方程，增添了些与经典CLL方程不同的数学物理性质，具有研究意义。
Abstract: In this paper, we based on the coupled Chen Lee Liu equation and obtained a class of integrable nonlocal CLL equations through a reduction. Starting from the Lax pair of integrable nonlocal CLL equation, a binary l Darboux transformation is constructed to obtain the expression of the solution under zero background. The classic Chen-Lee-Liu (CLL) equation is one of the most important inte-grable systems in mathematics and physics, which can be used to describe the propagation of puls-es in optical fibers. At present, many interesting solutions have been obtained by solving the CLL equation using methods such as Darboux transformation, Riemann Hilbert problem, and inverse scattering problem. This paper extends from the classical coupled CLL equation to the nonlocal CLL equation, adding some mathematical physics properties different from the classical CLL equation, which is of research significance.
文章引用：方日荣. 一类可积非局部CLL方程的求解[J]. 应用数学进展, 2023, 12(5): 2303-2309. https://doi.org/10.12677/AAM.2023.125234

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