The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations

doi:10.1016/j.chaos.2005.08.071

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	The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations
	Chen, Yong ; Yan, Zhenya
刊名	CHAOS SOLITONS & FRACTALS
	2006-08-01
卷号	29 期号:4 页码:948-964
ISSN号	0960-0779
DOI	10.1016/j.chaos.2005.08.071
英文摘要	In this paper, based on the close relationship between the Weierstrass elliptic function p(xi;g(2),g(3)) and nonlinear ordinary differential equation, a Weierstrass elliptic function expansion method is developed in terms of the Weierstrass elliptic function instead of many Jacobi elliptic functions. The mechanism is constructive and can be carried out in computer with the aid of computer algebra (Maple). Many important nonlinear wave equations arising from nonlinear science are chosen to illustrate this technique such as the new integrable Davey-Stewartson-type equation, the (2 + 1)dimensional modified KdV equation, the generalized Hirota equation in 2 + 1 dimensions, the Generalized KdV equation, the (2 + 1)-dimensional modified Novikov-Veselov equations, (2 + 1)-dimensional generalized system of modified KdV equation, the coupled Klein-Gordon equation, and the (2 + 1)-dimensional generalization of coupled nonlinear Schrodinger equation. As a consequence, some new doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Moreover solitary wave solutions and singular solitary wave solutions are also given as simple limits of doubly periodic solutions. These solutions may be useful to explain some physical phenomena. The algorithm is also applied to other many nonlinear wave equations. Moreover we also present the general form of the method. (c) 2005 Published by Elsevier Ltd.
WOS研究方向	Mathematics ; Physics
语种	英语
出版者	PERGAMON-ELSEVIER SCIENCE LTD
WOS记录号	WOS:000237763400019
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/3129]
专题	系统科学研究所
通讯作者	Chen, Yong
作者单位	1.Ningbo Univ, Ctr Nonlinear Sci, Ningbo 315211, Peoples R China 2.Ningbo Univ, Dept Math, Ningbo 315211, Peoples R China 3.Chinese Acad Sci, AMSS, Inst Syst Sci, Key Lab Math Mechanizat, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Chen, Yong,Yan, Zhenya. The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations[J]. CHAOS SOLITONS & FRACTALS,2006,29(4):948-964.
APA	Chen, Yong,&Yan, Zhenya.(2006).The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations.CHAOS SOLITONS & FRACTALS,29(4),948-964.
MLA	Chen, Yong,et al."The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations".CHAOS SOLITONS & FRACTALS 29.4(2006):948-964.