Conservation laws for variable coefficient nonlinear wave equations with power nonlinearities |
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| Authors: | Huang Ding-Jiang Zhou Shui-Geng Yang Qin-Min |
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| Affiliation: | Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China; School of Computer Science, Fudan University, Shanghai 200433, China; Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China |
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| 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. |
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| Keywords: | nonlinear wave equations conservation laws equivalence group symmetries |
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