Symbolic computation of exact solutions expressible in rational formal hyperbolic and elliptic functions for nonlinear partial differential equations

doi:10.1016/j.chaos.2005.10.002

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	Symbolic computation of exact solutions expressible in rational formal hyperbolic and elliptic functions for nonlinear partial differential equations
	Wang, Qi ; Chen, Yong
	2007
发表期刊	CHAOS SOLITONS & FRACTALS
ISSN	0960-0779
卷号	31 期号:2 页码:500-513
摘要	With the aid of symbolic computation, some algorithms are presented for the rational expansion methods, which lead to closed-form solutions of nonlinear partial differential equations (PDEs). The new algorithms are given to find exact rational formal polynomial solutions of PDEs in terms of Jacobi elliptic functions, solutions of the Riccati equation and solutions of the generalized Riccati equation. They can be implemented in symbolic computation system Maple. As applications of the methods, we choose some nonlinear PDEs to illustrate the methods. As a result, we not only can successfully obtain the solutions found by most existing Jacobi elliptic function methods and Tanh-methods, but also find other new and more general solutions at the same time. (c) 2005 Published by Elsevier Ltd.
DOI	10.1016/j.chaos.2005.10.002
语种	英语
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Interdisciplinary Applications ; Physics, Multidisciplinary ; Physics, Mathematical
WOS记录号	WOS:000240893400025
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5010
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Qi
作者单位	1.Dalian Univ Technol, Dept Appl Math, Dalian 116024, Peoples R China 2.Ningbo Univ, Dept Math, Nonlinear Sci Ctr, Ningbo 315211, Peoples R China 3.Chinese Acad Sci, Key Lab Math Mechanizat, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Wang, Qi,Chen, Yong. Symbolic computation of exact solutions expressible in rational formal hyperbolic and elliptic functions for nonlinear partial differential equations[J]. CHAOS SOLITONS & FRACTALS,2007,31(2):500-513.
APA	Wang, Qi,&Chen, Yong.(2007).Symbolic computation of exact solutions expressible in rational formal hyperbolic and elliptic functions for nonlinear partial differential equations.CHAOS SOLITONS & FRACTALS,31(2),500-513.
MLA	Wang, Qi,et al."Symbolic computation of exact solutions expressible in rational formal hyperbolic and elliptic functions for nonlinear partial differential equations".CHAOS SOLITONS & FRACTALS 31.2(2007):500-513.