(3)New sub-equation method to construct solitons and other solutions for perturbed nonlinear Schrödinger equation with Kerr law nonlinearity in optical fiber materials
PDF.pdf
Elsayed M.E. Zayed a, Abdul-Ghani Al-Nowehy b,*, Reham M.A. Shohib a
a Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
b Department of Mathematics, Faculty of Education and Science, Taiz University, Taiz, Yemen
Received 16 November 2018; received in revised form 7 December 2018; accepted 14 December 2018
Available online 20 December 2018
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.
© 2018 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Keywords: New sub-equation method; ( G,/G, 1/G )-expansion method; Generalized Riccati equation mapping method; Perturbed nonlinear Schrödinger equation; Exact solutions.