Symmetries,Integrability and Exact Solutions to the (2+1)-Dimensional Benney Types of Equations |
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Authors: | Han-Ze Liu Xiang-Peng Xin |
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Affiliation: | 1. School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China;2. Department of Mathematics, Binzhou University, Binzhou 256603, China |
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Abstract: | This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method. |
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Keywords: | Benney equation symmetry integrability exact solution shock wave solution |
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