The First Integral Method and its Application for Deriving the Exact Solutions of a Higher-Order Dispersive Cubic-Quintic Nonlinear Schrödinger Equation

Abstract

The objective of this article is to apply the first integral method to construct the exact solutions for a higher-order dispersive cubic-quintic nonlinear Schrödinger equation describing the propagation of extremely short pulses. Using a simple transformation, this equation can be reduced to a nonlinear ordinary differential equation (ODE). Various solutions of the ODE are obtained by using the first integral method. Further results are obtained by using a direct method. A comparison between our results and the well-known results is given.