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Abundant new non-travelling wave solutions for the (3+1) dimensional Boiti-Leon-Manna-Pempinelli equation
Jie Xin,Yuanqing Xu,Xiaoxiao Zheng
Keywords:extended homoclinic test approach; improved tanh function method; generalized Riccati equation; exact solutions.
Abstract:
      Seeking exact solutions of higher-dimensional nonlinear partial differential equations has recently received tremendous attention in mathematics and physics. In this paper, we investigate exact solutions of (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation which describes nonlinear wave propagations in incompressible fluid. Firstly, by means of extended homoclinic test approach, we get six kinds of non-traveling wave solutions of (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Then, combining the improved tanh function method and new ansatz solutions, we obtain abundant new exact non-traveling wave solutions of (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. These results combine not only many results obtained in other literatures, but also some new exact non-traveling wave solutions. Moreover, the exact kink wave, exact periodic solitary wave and singular solitary wave are given when arbitrary functions contained in the solutions are taken as some special functions.