Nonclassical potential solutions of partial differential equations

doi:10.1017/S0956792505005838

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	Nonclassical potential solutions of partial differential equations
	Bluman, GW ; Yan, ZY
	2005-04-01
发表期刊	EUROPEAN JOURNAL OF APPLIED MATHEMATICS
ISSN	0956-7925
卷号	16 页码:239-261
摘要	For a given scalar partial differential equation (PDE), a potential variable can be introduced through a conservation law. Such a conservation law yields an equivalent system (potential system) of PDEs with the given dependent variable and the potential variable as its dependent variables. Often there is also another equivalent scalar PDE (potential equation) with the potential variable as its dependent variable. The Nonclassical Method for obtaining solutions of PDEs is a generalization of the Classical Method for obtaining invariant solutions from point symmetries admitted by a given PDE. As a prototypical example, the nonlinear heat conduction equation is used to demonstrate that the Nonclassical Method applied to a potential equation can yield new solutions (nonclassical potential solutions) of a given PDE that are unobtainable as invariant solutions from admitted point symmetries of the given PDE, a related potential system or the potential equation, or from nonclassical solutions generated by applying the Nonclassical Method (tau equivalent to 1) to the given scalar PDE.
DOI	10.1017/S0956792505005838
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000231338800004
出版者	CAMBRIDGE UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1897
专题	系统科学研究所
通讯作者	Bluman, GW
作者单位	1.Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada 2.Chinese Acad Sci, AMSS, Key Lab Math Mechanizat, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Bluman, GW,Yan, ZY. Nonclassical potential solutions of partial differential equations[J]. EUROPEAN JOURNAL OF APPLIED MATHEMATICS,2005,16:239-261.
APA	Bluman, GW,&Yan, ZY.(2005).Nonclassical potential solutions of partial differential equations.EUROPEAN JOURNAL OF APPLIED MATHEMATICS,16,239-261.
MLA	Bluman, GW,et al."Nonclassical potential solutions of partial differential equations".EUROPEAN JOURNAL OF APPLIED MATHEMATICS 16(2005):239-261.