Soliton solutions to the nonlinear higher dimensional Kadomtsev-Petviashvili equation through the new Kudryashov's technique

Abstract

In this paper, we studied the (3 + 1)-dimensional nonlinear Kadomtsev-Petviasvili equation (3D-KPE) that is utilized in order to describe 3D solitons in weakly dispersive media, long wavelength water waves with weak nonlinear restoring forces, waves in ferromagnetic media, nonlinear wave propagation in supefluids, plasma physics and fluid dynamics by using the recently presented the new Kudryashov's method. We successfully applied the new Kudryashov's scheme to the investigated problem for the first time to achieve bright and singular soliton; besides, we showed that the technique is effective, easily applicable, and reliable in solving such nonlinear problems. Moreover, the necessary comments were given by obtaining appropriate soliton solutions and presented 3D and 2D graphics.