| 耦合KdV方程的约化及求解 |
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| 引用本文： | 程雪苹,李金玉,薛江蓉.耦合KdV方程的约化及求解[J].物理学报,2011,60(11):110204-110204. |
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| 作者姓名： | 程雪苹 李金玉 薛江蓉 |
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| 作者单位： | 1. 浙江海洋学院数理与信息学院物理系,舟山 316004;
2. 上海交通大学物理系,上海 200240 |
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| 基金项目： | 浙江省自然科学基金(批准号:Y1100088)、国家自然科学基金(批准号:11047155)和浙江海洋学院校级专项基金资助的课题. |
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| 摘 要： | 利用Clarkson和Kruskal(CK)直接方法,对耦合KdV方程进行相似约化,同时从李群出发对该约化方程作了群论解释.进一步地,借助Ablowitz-Ramani-Segur(ARS)算法对耦合方程展开Painlevé测试,找到了3个Painlevé可积模型.最后通过形变映射法,求得耦合KdV方程的准确解析解.
关键词：
耦合KdV方程
CK直接法
Painlevé分析法
准确解析解
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| 关 键 词： | 耦合KdV方程 CK直接法 Painlevé分析法 准确解析解 |
| 收稿时间： | 4/1/2011 12:00:00 AM |
Coupled KdV equation: similarity reduction and analytical solution |
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| Cheng Xue-Ping,Li Jin-Yu and Xue Jiang-Rong.Coupled KdV equation: similarity reduction and analytical solution[J].Acta Physica Sinica,2011,60(11):110204-110204. |
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| Authors: | Cheng Xue-Ping Li Jin-Yu and Xue Jiang-Rong |
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| Institution: | Physics,Mathematics and Information College of Zhejiang Ocean University, Zhoushan 316004, China;Department of Physics, Shanghai Jiaotong University,Shanghai 200240, China;Physics,Mathematics and Information College of Zhejiang Ocean University, Zhoushan 316004, China;Physics,Mathematics and Information College of Zhejiang Ocean University, Zhoushan 316004, China |
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| Abstract: | Using the CK direct method, we obtain the similarity reduction of coupled KdV equation, which is then explained in detail by group theory. To check the Painlevé integrability of coupled KdV equation, the reduction equation is also classified by means of the Painlevé test, and three types of P-integrable models are found. Finally, it is shown that the coupled KdV equation has kinds of traveling wave solutions, including conoidal periodic wave solution, soliton solution, and so on. |
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| Keywords: | coupled KdV equation CK direct method Painlevé test exact analytical solution |
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