Compact and noncompact structures of a three-dimensional 3DKP equation with nonlinear dispersion

In this paper, we investigate exact-special solutions of the three-dimensional Kadomtsev–Petviashvili equation ( 3 DKP ( m , n ) ) with nonlinear dispersion. We use the ansatz method and the Exp-function method for this equation. So, we get general formulae for the compactons, solitary patterns, solitons and periodic solutions. In addition, we obtain a new travelling wave solution for the 3 DKP ( 2 , 1 ) equation by the Exp-function method.