| (2+1)维广义浅水波方程类孤子解和类周期解 |
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| 引用本文： | 梅建琴,张鸿庆. (2+1)维广义浅水波方程类孤子解和类周期解[J]. 大连理工大学学报, 2005, 45(4): 612-616 |
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| 作者姓名： | 梅建琴 张鸿庆 |
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| 作者单位： | 大连理工大学,应用数学系,辽宁,大连,116024;大连理工大学,应用数学系,辽宁,大连,116024 |
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| 基金项目： | 国家重点基础研究发展计划(973计划);国家自然科学基金 |
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| 摘 要： | 在Riccati方程方法的基础上提出了新的广义投射Riccati方程展开法及其算法.该方法直接而有效,通过适当的变换将非线性发展方程转化为易于求解的微分方程组,从而可用来构造非线性发展方程更多新的精确解.利用这个方法研究了(2 1)维浅水波方程,并得到了许多新的精确解,其中包括类孤子解和类周期解.该算法可以用于构造其他更多非线性发展方程(组)的精确解.
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| 关 键 词： | 精确解 (2+1)维广义浅水波方程 类孤子解 类周期解 |
| 文章编号： | 1000-8608（2005）04-0612-05 |
| 收稿时间： | 2004-07-12 |
| 修稿时间： | 2004-07-12 |
Soliton-like and periodic-like solutions of (2+1)-dimensional generalization of shallow water wave equation |
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| MEI Jian-qin,ZHANG Hong-qing. Soliton-like and periodic-like solutions of (2+1)-dimensional generalization of shallow water wave equation[J]. Journal of Dalian University of Technology, 2005, 45(4): 612-616 |
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| Authors: | MEI Jian-qin ZHANG Hong-qing |
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| Abstract: | Based on a system of Riccati equations, a new generally projectiveRiccati equation expansion method is presented. It is very direct and powerfuland can be used to construct more new exact solutions of nonlinearevolutionary equations in mathematical physics. The (2 1)-dimensionalgeneralization of the shallow water wave equation is chosen to illustrate thealgorithm such that more families of new exact solutions are obtained, whichcontain soliton-like and periodic-like solutions. This algorithm can also beapplied to other nonlinear differential equations. |
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| Keywords: | exact solution (2 1)-dimensional generalization of the shallow water wave equation soliton-like solution periodic-like solution |
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