Conservation laws for variable coefficient nonlinear wave equations with power nonlinearities

doi:10.1088/1674-1056/20/7/070202

中国物理B ›› 2011, Vol. 20 ›› Issue (7): 70202-070202.doi: 10.1088/1674-1056/20/7/070202

Conservation laws for variable coefficient nonlinear wave equations with power nonlinearities

杨勤民¹, 黄定江², 周水庚³

(1)Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China; (2)Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China;Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China; (3)School of Computer Science, Fudan University, Shanghai 200433, China

收稿日期:2010-08-03 修回日期:2011-02-04 出版日期:2011-07-15 发布日期:2011-07-15

Conservation laws for variable coefficient nonlinear wave equations with power nonlinearities

Huang Ding-Jiang(黄定江)^a)b)c)†, Zhou Shui-Geng(周水庚)^b)c), and Yang Qin-Min(杨勤民)^a)

^a Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China; ^b School of Computer Science, Fudan University, Shanghai 200433, China; ^c Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China

Received:2010-08-03 Revised:2011-02-04 Online:2011-07-15 Published:2011-07-15

摘要/Abstract

摘要： Conservation laws for a class of variable coefficient nonlinear wave equations with power nonlinearities are investigated. The usual equivalence group and the generalized extended one including transformations which are nonlocal with respect to arbitrary elements are introduced. Then, using the most direct method, we carry out a classification of local conservation laws with characteristics of zero order for the equation under consideration up to equivalence relations generated by the generalized extended equivalence group. The equivalence with respect to this group and the correct choice of gauge coefficients of the equations play the major roles for simple and clear formulation of the final results.

关键词: nonlinear wave equations, conservation laws, equivalence group, symmetries

Abstract: Conservation laws for a class of variable coefficient nonlinear wave equations with power nonlinearities are investigated. The usual equivalence group and the generalized extended one including transformations which are nonlocal with respect to arbitrary elements are introduced. Then, using the most direct method, we carry out a classification of local conservation laws with characteristics of zero order for the equation under consideration up to equivalence relations generated by the generalized extended equivalence group. The equivalence with respect to this group and the correct choice of gauge coefficients of the equations play the major roles for simple and clear formulation of the final results.

Key words: nonlinear wave equations, conservation laws, equivalence group, symmetries

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

02.30.Jr (Partial differential equations)

黄定江, 周水庚, 杨勤民. Conservation laws for variable coefficient nonlinear wave equations with power nonlinearities[J]. 中国物理B, 2011, 20(7): 70202-070202.

Huang Ding-Jiang(黄定江), Zhou Shui-Geng(周水庚), and Yang Qin-Min(杨勤民). Conservation laws for variable coefficient nonlinear wave equations with power nonlinearities[J]. Chin. Phys. B, 2011, 20(7): 70202-070202.

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Conservation laws for variable coefficient nonlinear wave equations with power nonlinearities

Conservation laws for variable coefficient nonlinear wave equations with power nonlinearities

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