Bäcklund 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 be reduced to the standard KP equation and the well-know (3+1)-dimensional equation. In making use of the Lax pair transformation, a Bäcklund transformation of the generalized (3+1)-dimensional KP equation is constructed and some soliton solutions are produced. Finally, a superposition formula is singled out as well by making use of the Bäcklund transformation. As far as we know, the work presented in this paper has not been studied up to now.