CLASSIFICATION OF LOCAL AND NONLOCAL SYMMETRIES OF FOURTH-ORDER NONLINEAR EVOLUTION EQUATIONS

被引:9
|
作者
Huang, Qing [1 ,2 ]
Qu, C. Z. [1 ,2 ]
Zhdanov, R. [3 ]
机构
[1] NW Univ Xian, Dept Math, Xian 710069, Peoples R China
[2] NW Univ Xian, Ctr Nonlinear Studies, Xian 710069, Peoples R China
[3] BIO Key Int, Eagan, MN 55121 USA
关键词
evolution equation; quasi-local symmetry; nonlocal symmetry; Lie group; Lie algebra; PARTIAL-DIFFERENTIAL EQUATIONS; LIE-ALGEBRAS;
D O I
10.1016/S0034-4877(10)00017-0
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In this paper, we consider the group classification of local and quasi-local symmetries for a general fourth-order evolution equations in one spatial variable. Following the approach developed in [26], we construct all inequivalent evolution equations belonging to the class under study which admit either semi-simple Lie groups or solvable Lie groups. The obtained lists of invariant equations (up to a local change of variables) contain both the well-known equations and a variety of new ones possessing rich symmetry. Based on the results on the group classification for local symmetries, the group classification for quasi-local symmetries of the equations is also given.
引用
收藏
页码:337 / 366
页数:30
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