B¨acklund Transformation for Solving a (3+1)-Dimensional Integrable Equation

A new generalized (3+1)-dimensional Kadomtsev-Petviashvil (3dKP) equation is derived from the inverse scattering transform method. This equation can reduce to the standard KP equation and the well-know (3+1)- dimensional equation. Making use of the Lax pair transformation, a B¨acklund transformation of the generalized (3+1)- dimensional KP equation is constructed and some soliton solutions are produced. Finally, a superposition formula by making use of the Ba¨cklund transformation is singled out as well. As we know that such the work presented in the paper is not studied up to now.