Nonlocal Symmetries and Interaction Solutions for Potential Kadomtsev-Petviashvili Equation |
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Authors: | Bo Ren Jun Yu Xi-Zhong Liu |
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Institution: | Institute of Nonlinear Science, Shaoxing University, Shaoxing 312000, China |
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Abstract: | The nonlocal symmetry for the potential Kadomtsev-Petviashvili (pKP) equation is derived by the truncated Painlevé analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing the auxiliary dependent variable. Thanks to localization process, the finite symmetry transformations related with the nonlocal symmetry are obtained by solving the prolonged systems. The inelastic interactions among the multiple-front waves of the pKP equation are generated from the finite symmetry transformations. Based on the consistent tanh expansion method, a nonauto-Bäcklund transformation (BT) theorem of the pKP equation is constructed. We can get many new types of interaction solutions because of the existence of an arbitrary function in the nonauto-BT theorem. Some special interaction solutions are investigated both in analytical and graphical ways. |
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Keywords: | potential Kadomtsev-Petviashvili equation nonlocal symmetry front wave consistent tanh expansion method |
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