| Coupled Nonlinear Schrodinger Equation： Symmetries and Exact Solutions |
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| 基金项目： | The project supported by the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institute and the National Natural Science Foundation of China under Grant Nos. 10735030 and 90503006
We are indebted to Drs. Z.L. Li and J.H. Li for their helpful discussions. |
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| 摘 要： | The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.
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| 关 键 词： | 耦合非线性薛定谔方程 对称性 精确解 NLS方程 大气重力波 伽利略变换 常微分方程 三角函数解 |
| 收稿时间： | 2008-04-02 |
Coupled Nonlinear Schrödinger Equation: Symmetries and Exact Solutions |
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| Authors: | LIU Ping LOU Sen-Yue |
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| Institution: | 1.Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China
;2.Department of Electronic Engineering, University of Electronic Science and Technology of China Zhongshan Institute, Zhongshan 528402, China
;3.Department of Physics, Ningbo University, Ningbo 315211, China |
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| Abstract: | The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrödinger (CNLS) equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries. |
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| Keywords: | coupled nonlinear SchrSdinger equation classical Lie group approach symmetry exact solution |
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