Generation of Nonlinear Evolution Equations by Reductions of the Self-Dual Yang–Mills Equations

作     者：张玉峰 Hon-Wah Tam 

作者机构：College of Sciences China University of Mining and Technology Department of Computer Science Hong Kong Baptist University 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2014年第61卷第2期

页      面：203-206页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 

基　　金：Supported by the Fundamental Research Funds for the Central Universities(2013XK03) the National Natural Science Foundation of China under Grant No.11371361 

主　　题：self-dual Yang-Mills equation Lax pair (2+ 1)-dimensional integrable system integrable coupling 

摘      要：With the help of some reductions of the self-dual Yang Mills(briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of(2 + 1)-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation,the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new(2 + 1)-dimensional nonlinear integrable systems, in particular, obtains a kind of(2 + 1)-dimensional integrable couplings of a new(2 + 1)-dimensional integrable nonlinear equation.