| CONDITIONAL SIMILARITY REDUCTION APPROACH: JIMBO－MIWA EQUATION |
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| 引用本文： | 楼森岳,唐晓艳.CONDITIONAL SIMILARITY REDUCTION APPROACH: JIMBO－MIWA EQUATION[J].中国物理 B,2001,10(10):897-901. |
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| 作者姓名： | 楼森岳 唐晓艳 |
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| 作者单位： | (1)Department of Physics, Ningbo University, Ningbo 315211, China; Department of Physics, Shanghai Jiaotong University, Shanghai 200030, China; (2)Department of Physics, Shanghai Jiaotong University, Shanghai 200030, China |
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| 基金项目： | Project supported by the National Natural Science Foundation for Outstanding Young Scientists of China (Grant No. 19925522), by the Doctoral Program Foundation of Institutions of Higher Education of China (Grant No. 2000024832) and by the Natural Science Foundation of Zheijiang Province, China. |
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| 摘 要： | The direct method developed by Clarkson and Kruskal (1989 J. Math. Phys. 30 2201) for finding the symmetry reductions of a nonlinear system is extended to find the conditional similarity solutions. Using the method of the Jimbo－Miwa (JM) equation, we find that three well-known (2+1)-dimensional models－the asymmetric Nizhnik--Novikov－Veselov equation, the breaking soliton equation and the Kadomtsev-Petviashvili equation－can all be obtained as the conditional similarity reductions of the JM equation.
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| 关 键 词： | conditional similarity reductions Jimbo－Miwa equation Kadomtsev－Petviashvili equation breaking soliton equation asymmetric Nizhnik－Novikov－Veselov equation |
| 收稿时间： | 2000-07-20 |
CONDITIONAL SIMILARITY REDUCTION APPROACH: JIMBO--MIWA EQUATION |
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| Lou Sen-yue and Tang Xiao-yan.CONDITIONAL SIMILARITY REDUCTION APPROACH: JIMBO--MIWA EQUATION[J].Chinese Physics B,2001,10(10):897-901. |
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| Authors: | Lou Sen-yue and Tang Xiao-yan |
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| Affiliation: | Department of Physics, Ningbo University, Ningbo 315211, China; Department of Physics, Shanghai Jiaotong University, Shanghai 200030, China |
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| Abstract: | The direct method developed by Clarkson and Kruskal (1989 J. Math. Phys. 30 2201) for finding the symmetry reductions of a nonlinear system is extended to find the conditional similarity solutions. Using the method of the Jimbo－Miwa (JM) equation, we find that three well-known (2+1)-dimensional models－the asymmetric Nizhnik－Novikov－Veselov equation, the breaking soliton equation and the Kadomtsev-Petviashvili equation－can all be obtained as the conditional similarity reductions of the JM equation. |
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| Keywords: | conditional similarity reductions Jimbo－Miwa equation Kadomtsev－Petviashvili equation breaking soliton equation asymmetric Nizhnik－Novikov－Veselov equation |
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