Symbolic computation and new families of exact non-travelling wave solutions to (3Â +Â 1)-dimensional Kadomstev-Petviashvili equation

In this paper, the improved tanh function method in [F.D. Xie, Y. Zhang, Z.S. Lü, Chaos, Solitons & Fractals 24 (2005) 257] is further improved by constructing new ansatz solution of the considered equation. As its application, the (3 + 1)-dimensional Kadomstev-Petviashvili equation is considered and abundant new exact non-travelling wave solutions are obtained.