Painlevé analysis, soliton solutions and lump-type solutions of the (3+1)-dimensional generalized KP equation

The Painlevé analysis is applied and the multi-soliton criterion is presented to test the integrability of the (3+1)-dimensional generalized KP equation derived from a Hirota bilinear equation. It is shown that the considered equation does not pass the well known Painlevé test and it is only integrable in a conditional sense. Solitary wave solutions are shown to interact each other like solitons in multiple wave collisions unless some additional conditions are imposed. Moreover, we analyze a class of analytical rational lump-type solutions in detail, which are generated from positive quadratic polynomial function and rationally localized in many directions in the space, based upon the Hirota bilinear form.