2+1维广义浅水波方程的类孤子解与周期解

数学物理学报 ›› 2005, Vol. 25 ›› Issue (6): 784-788.

2+1维广义浅水波方程的类孤子解与周期解

梅建琴, 张鸿庆

大连理工大学应用数学系大连 116024 中国科学院数学机械化实验室北京 100080

出版日期:2005-12-24 发布日期:2005-12-24
基金资助:
国家自然科学基金(Grant No.10072013,10072189)资助

Some Soliton like and Periodic Solutions for a (2+1) dimensional Generalization of Shallow Water Wave Equation

MEI Jian-Qin, ZHANG Hong-Qiang

Online:2005-12-24 Published:2005-12-24
Supported by:
国家自然科学基金(Grant No.10072013,10072189)资助

摘要/Abstract

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。

关键词: (2+1)维广义浅水波方程;类孤子解;周期解

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 differ ential equations in mathematical physics. The (2+1)dimensional eneralization of shallow water wave equation is chosen to illustrate the algorithm such that m ore families of new exact solutions are obtained, which contain soliton\|like and periodic solutions. This algorithm can also be applied to other nonlinear diff erential equations.

Key words: (2+1)dimensional generalization of shallow water wave , equaiton, Soliton like solution, Periodic solution.

中图分类号:

35Q51

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, 2005, 25(6): 784-788.

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,Series A, 2005, 25(6): 784-788.

参考文献

[1]Ablowitz M J, Clarkson P A. Solitons, Nonlinear Evolution Equations and Inverse Scattering Tra nsform. Cambridge: Cambridge University Press, 1990

[2]Konopelchenko B G. Solitons in Multidimensions. Singapore: World Scientific Press,1993

[3]Yan Z Y. The extended Jacobin elliptic function expansion method and its appli cation in the generalized Hirota Satsuma coupled KdV system.Chaos Solitons and Fractals, 2003,15:575-583

[4]Parkes E J, Duffy B R. An automated Tanhfunction method for finding solita ry wave solutions to non linear evolution equations. Comp Phys Comm,
1996,98: 288-300

[5]Yan Z Y. New explicit and exact travelling wave solutions for a system of varia nt Boussinesq equations in mathematical physics.Phys Lett A,1999,252:291-296

[6]Gao Y T,Tian B. Generalized hyperbolicfunction method with computerized symb olic computation to construct the solitonic solutions to nonlinear
equations of mathematical physics. Comput Phys Comm,2001,133:158-164

[7]Yan Z Y. Generalized method and its application in the higherorder nonlinear S chr
[AKo¨D]dinger equation in nonlinear optical fibres.Chaos, Solitons and Fractals, 2003,16:759-766

[8]Senthilvelan M. On the extended applications of homogenous balance method.Applied Mathematics and Computation, 2001,123:381-388

[9]Tian B, Gao Y T. Solitonlike Solutions for a (2+1)dimensional generalizatio n of the shallow water wave equations. Chaos, Solitons and Fractals,1996,7(9):1497-1499

[10]Gao Y T, Tian B. Generalized tanh method with symbolic computation and generali zed shallow water wave equation. Computers and Mathematics with Applications,1997,33(4):115-118

[11]Ghosh Kamal Kumar, Debnath Lokenath.Some exact solutions of non linear shallow water equations.International Journalof Nonlinear echanics,1997,32(3):633-636
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