Bright and dark soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili equation and generalized Benjamin equation

Abstract

In this paper, we obtain the 1-soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and the generalized Benjamin equation. By using two solitary wave ansatz in terms of sechp and \(\tanh^{p}\) functions, we obtain exact analytical bright and dark soliton solutions for the considered model. These solutions may be useful and desirable for explaining some nonlinear physical phenomena in genuinely nonlinear dynamical systems.