A comparative study of approximate symmetry and approximate homotopy symmetry to a class of perturbed nonlinear wave equations

doi:10.1016/j.na.2011.03.005

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	A comparative study of approximate symmetry and approximate homotopy symmetry to a class of perturbed nonlinear wave equations
	Zhang, Zhiyong 1,2; Chen, Yufu 2
	2011-09-01
发表期刊	NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
ISSN	0362-546X
卷号	74 期号:13 页码:4300-4318
摘要	A comparative study of approximate symmetry and approximate homotopy symmetry to a class of perturbed nonlinear wave equations is performed. First, complete infinite-order approximate symmetry classification of the equation is obtained by means of the method originated by Fushchich and Shtelen. An optimal system of one-dimensional subalgebras is derived and used to construct general formulas of approximate symmetry reductions and similarity solutions. Second, we study approximate homotopy symmetry of the equation and construct connections between the two symmetry methods for the first-order and higher-order cases, respectively. The series solutions derived by the two methods are compared. (c) 2011 Elsevier Ltd. All rights reserved.
关键词	Approximate symmetry Optimal system Reduction Approximate homotopy symmetry
DOI	10.1016/j.na.2011.03.005
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000291006900002
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/11296
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Zhiyong
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Grad Univ, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Zhiyong,Chen, Yufu. A comparative study of approximate symmetry and approximate homotopy symmetry to a class of perturbed nonlinear wave equations[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,2011,74(13):4300-4318.
APA	Zhang, Zhiyong,&Chen, Yufu.(2011).A comparative study of approximate symmetry and approximate homotopy symmetry to a class of perturbed nonlinear wave equations.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,74(13),4300-4318.
MLA	Zhang, Zhiyong,et al."A comparative study of approximate symmetry and approximate homotopy symmetry to a class of perturbed nonlinear wave equations".NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 74.13(2011):4300-4318.