| 2+1维广义浅水波方程的类孤子解与周期解 |
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| 引用本文： | 梅建琴,张鸿庆.2+1维广义浅水波方程的类孤子解与周期解[J].数学物理学报(A辑),2005,25(6):784-788. |
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| 作者姓名： | 梅建琴 张鸿庆 |
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| 作者单位： | [1]大连理工大学应用数学系,大连116024 [2]中国科学院数学机械化实验室,北京100080 |
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| 基金项目： | 国家自然科学基金（Grant No.10072013,10072189）资助 |
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| 摘 要： | 该文基于一个Riccati方程组，提出了一个新的广义投影Ric cati展开法，该方法直接简单并能构造非线性微分方程更多的新的解析解。利用该算法研究了(2+1)维广义浅水波方程，并求得了许多新的精确解，包括类孤子解和周期解。该算法也能应用到其它非线性微分方程中。
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| 关 键 词： | (2+1)维广义浅水波方程 类孤子解 周期解 |
| 文章编号： | 1003-3998(2005)06-784-05 |
| 收稿时间： | 2003-12-06 |
| 修稿时间： | 2004-10-20 |
Some Soliton like and Periodic Solutions for a (2+1) dimensional Generalization of Shallow Water Wave Equation |
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| MEI Jian-Qin,ZHANG Hong-Qiang.Some Soliton like and Periodic Solutions for a (2+1) dimensional Generalization of Shallow Water Wave Equation[J].Acta Mathematica Scientia,2005,25(6):784-788. |
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| Authors: | MEI Jian-Qin ZHANG Hong-Qiang |
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| Institution: | 1 Department of Applied Mathematics, Dalian University of Technology, Dalian 116024;2Key Laboratory of Mathematics Mechanization, CAS , Beijing 100080 |
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| Abstract: | In this paper, based on a system of Riccati equations, a newly general projective Riccati equaiton expansion method is presented. It is direct and can be used to construct more new exact solutions of nonlinear differential equations in mathematical physics. The (2 1)-dimensional generalization of shallow water wave equation is chosen to illustrate the algorithm such that more families of new exact solutions are obtained, which contain soliton-like and periodic solutions. This algorithm can also be applied to other nonlinear differential equations. |
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| Keywords: | (2 1)-dimensional generalization of shallow water wave equaiton Soliton-like solution Periodic solution |
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