Painlev'e integrability, bilinearization and exact solutions of the new (3+1) - dimensional generalized Kadomstev-Petviashvili equation

Abstract

New generalized Kadomstev-Petviashvili (ngKP) equation in $(3+1)$ - dimensions, describing long waves of small amplitude with slow dependence on the transverse coordinate, is examined by locating singularity points with the help of Painlev\'{e} analysis. Despite that Painlev\'{e} test fails to prove the integrability of the ngKP equation, Bell polynomial approach and Painlev\'{e} expansion is truncated to construct its bilinear form. Novel test function has been appointed to explore the exact solutions of ngKP equation. The obtained solutions possess rich spatial structures due to the presence of abundant arbitrary constants. It is worthy to note that the solutions are absolutely new and cannot be obtained from the ones which already exist in the literature.