| Finite Symmetry Transformation Groups and Some Exact Solutions to （2＋1）-Dimensional Cubic Nonlinear SchrSdinger Equantion |
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| 作者姓名： | LI Biao LI Yu-Qi CHEN Yong |
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| 作者单位： | [1]Nonlinear Science Center, Ningbo University, Ningbo 315211, China [2]Institute of Theoretical Computing, East China Normal University, Shanghai 200062, China [3]Key Laboratory of Mathematics Mechanization, Chinese Academy of Sciences, Beijing 100080, China |
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| 基金项目： | The project supported by K.C. Wong Magna Fund in Ningbo University, National Natural Science Foundation of China under Grant Nos. 10747141 and 10735030, Zhejiang Provincial Natural Science Foundations of China under Grant No. 605408, Ningbo Natural Science Foundation under Grant Nos. 2007A610049 and 2006A610093, and National Basic Research Program of China （973 Program 2007CB814800）, Program for Changjiang Scholars and Innovative Research Team in University （IRTO734） |
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| 摘 要： | Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a （2＋ l）-dimensional cubic nonlinear Schrodinger （NLS） equation and its corresponding cylindrical NLS equations are presented. Nine related linear independent infinitesimal generators can be obtained from the finite symmetry transformation groups by restricting the arbitrary constants in infinitesimal forms. Some exact solutions are derived from a simple travelling wave solution.
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| 关 键 词： | 立方非线性 对称变换 有限 精确解 符号计算 线性独立 直接法 薛定谔 |
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