| Symmetry Reduction and Exact Solutions of the （3＋1）-Dimensional Breaking Soliton Equation |
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| 作者姓名： | WANG Ling ;DONG Zhong-Zhou |
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| 作者单位： | [1]Department of Mathematics and Computer Science, Chizhou University, Chizhou 247000, China; [2]Shanghai Key Laboratory of Trustworthy 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 National Natural Science Foundation of China under Grant No. 10735030, Shanghai Leading Academic Discipline Project under Grant No. B412, Natural Science Foundations of Zhejiang Province of China under Grant No. Y604056 and the Doctoral Foundation of Ningbo City under Grant No. 2005A61030
Acknowledgments The authors would like to express sincere thanks to Prof. Chen Yong for his useful comments. |
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| 摘 要： | By means of the generalized direct method, a relationship is constructed between the new solutions and the old ones of the （3＋1）-dimensional breaking soliton equation. Based on the relationship, a new solution is obtained by using a given solution of the equation. The symmetry is also obtained for the （3＋1）-dimensional breaking soliton equation. By using the equivalent vector of the symmetry, we construct a seven-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, the （3＋1）-dimensional breaking soliton equation is reduced and some solutions to the reduced equations are obtained. Furthermore, some new explicit solutions are found for the （3＋ 1）-dimensional breaking soliton equation.
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| 关 键 词： | 孤立子 广义直接方法 对称性 求解方法 |
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