| Non-Lie Symmetry Groups of （2＋1）-Dimensional Nonlinear Systems |
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| 作者姓名： | MA Hong-Cai LOU Sen-Yue |
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| 作者单位： | [1]Department of Mathematics, Donghua University, Shanghai 200051, China [2]Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China [3]Center of Nonlinear Science, Ningbo University, Ningbo 315211, China |
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| 基金项目： | The project supported by the National 0utstanding Youth Foundation of China under Grant No. 19925522 and the National Natural Science Foundation of China under Grant Nos. 90203001, 10475055. The authors are in debt to thank helpful discussions with Drs. X.Y. Tang, C.L. Chen, Y. Chen, H.C. Hu, X.M. Qian, B. Tong, and W.R. Cai. |
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| 摘 要： | A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only speciai cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches.
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| 关 键 词： | 非李对称群 对称性 CK直接法 精确解 非线性数学物理系统 |
| 收稿时间： | 2006-02-23 |
| 修稿时间： | 2006-02-23 |
Non-Lie Symmetry Groups of (2+1)-Dimensional Nonlinear Systems |
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| MA Hong-Cai LOU Sen-Yue.Non-Lie Symmetry Groups of (2+1)-Dimensional Nonlinear Systems[J].Communications in Theoretical Physics,2006,46(6):1005-1010. |
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| Authors: | MA Hong-Cai and LOU Sen-Yue |
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| Institution: | 1. Department of Mathematics, Donghua University, Shanghai 200051, China
;2. Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China
;3. Center of Nonlinear Science, Ningbo University, Ningbo 315211, China |
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| Abstract: | A modified direct method is developed to find finite symmetry
groups of nonlinear mathematical physics systems. Applying the
modified direct method to the well-known (2+1)-dimensional
asymmetric Nizhnik-Novikov-Vesselov
equation and Nizhnik-Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry
groups obtained via traditional Lie approaches are only special
cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those
obtained via the standard approaches. |
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| Keywords: | symmetry groups CK direct method symmetries exact solution |
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