The First Integral Method to the Improved Perturbed Nonlinear Schrödinger’s Equation with the Dual-Power Nonlinearity

Abstract

The first integral method is an effective method to obtain exact solutions of some nonlinear partial differential equations. In this paper, first integral method is used to solve the improved perturbed nonlinear Schrödinger’s equation with the dual-power law nonlinearity. As a result, we obtain explicit and exact traveling wave solutions with some free parameters. For some specific choice of parameters, our exact solutions reduce to the solutions of nonlinear Schrödinger’s equation with parabolic law nonlinearity. Further, we compare our results with the results derived by the Sub-ODE method and New mapping method. The behaviours of exact solutions are presented by figures. Our results in this article confirm that the first integral method is an efficient technique for an analytic treatment of a wide variety of nonlinear partial differential equations in mathematical physics.