A new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation

We introduce a new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation. We use the simplified Hirota's direct method to derive multiple-soliton solutions for the new model with the coefficients of the spatial variables which are left free. We show that the phase shifts depend on all these coefficients. We prove that the new model fails the Painlev, integrability test although it gives multiple-soliton solutions. Moreover, for , this new model reduces to the potential KdV equation, which we will examine as well.