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Group properties of generalized quasi-linear wave equations |
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| Authors: | Ding-jiang Huang Shuigeng Zhou |
| Institution: | a School of Computer Science, Fudan University, Shanghai 200433, China b Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai 200433, China c Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China |
| Abstract: | In this paper, complete group classification of a class of (1+1)-dimensional generalized quasi-linear wave equations is performed by using the Lie-Ovsiannikov method, additional equivalent transformation and furcate split method. Lie reductions of some truly ‘variable coefficient’ wave equations which are singled out from the classification results are investigated. Some classes of exact solutions of these ‘variable coefficient’ wave equations are constructed by means of both the reductions and the additional equivalent transformations. The nonclassical symmetries to the generalized quasi-linear wave equation are also studied. This enabled to obtain some exact solutions of the wave equations which are invariant under certain conditional symmetries. |
| Keywords: | Generalized quasi-linear wave equations Group classification Symmetry reduction Nonclassical symmetries Exact solutions |
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