Traveling Wave Solutions of the Nonlinear ( 3 + 1 ) -Dimensional Kadomtsev-Petviashvili Equation Using the Two Variables ( G ′ / G , 1 / G ) -Expansion Method

Abstract

The two variables $(G^{\prime }/G,1/G)$-expansion method is proposed in this paper to construct new exact traveling wave solutions with parameters of the nonlinear $(3+1)$-dimensional Kadomtsev-Petviashvili equation. This method can be considered as an extension of the basic $(G^{\prime }/G)$-expansion method obtained recently by Wang et al. When the parameters are replaced by special values, the well-known solitary wave solutions and the trigonometric periodic solutions of this equation were rediscovered from the traveling waves.