New sub-equation method to construct solitons and other solutions for perturbed nonlinear Schrödinger equation with Kerr law nonlinearity in optical fiber materials

Abstract

In a previous work, Zayed and Al-Nowehy have applied the Riccati equation mapping method combined with the generalized extended (G′/G)-expansion method and found new exact solutions of the nonlinear KPP equation. In the present article, we propose a different method, namely, a new sub-equation method consists of the Riccati equation mapping method and the (G′/G, 1/G)-expansion method to find new exact solutions of the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity in optical fiber materials. This proposed method is not found elsewhere. Hyperbolic, trigonometric and rational function solutions are given. New solutions of the generalized Riccati equation are presented for the first time which are not reported previously. The solutions of the given nonlinear equation can be applied in ocean engineering for calculating the height of tides in the ocean.