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| Generation of Nonlinear Evolution Equations by Reductions of the Self-Dual Yang–Mills Equations | |
| 引用本文： | 张玉峰,Hon-Wah Tam. Generation of Nonlinear Evolution Equations by Reductions of the Self-Dual Yang–Mills Equations[J]. 理论物理通讯, 2014, 61(2): 203-206 |
| 作者姓名： | 张玉峰 Hon-Wah Tam |
| 基金项目： | Supported by the Fundamental Research Funds for the Central Universities(2013XK03);the National Natural Science Foundation of China under Grant No.11371361 |
| 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. |
| 关 键 词： | 非线性发展方程 变系数Burgers方程 自对偶 减排量 可积系统 热传导方程 非线性方程 Lax对 |
| 收稿时间： | 2013-06-14 |
Generation of Nonlinear Evolution Equations by Reductions of the Self-Dual Yang-Mills Equations |
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| ZHANG Yu-Feng,Hon-Wah Tam. Generation of Nonlinear Evolution Equations by Reductions of the Self-Dual Yang-Mills Equations[J]. Communications in Theoretical Physics, 2014, 61(2): 203-206 | |
| Authors: | ZHANG Yu-Feng Hon-Wah Tam |
| Affiliation: | 1. College of Sciences, China University of Mining and Technology, Xuzhou 221116, China;2. Department of Computer Science, Hong Kong Baptist University, Hong Kong, China |
| Abstract: | 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. |
| Keywords: | self-dual Yang-Mills equation Lax pair （2＋ 1）-dimensional integrable system integrable coupling |
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