Eur. Phys. J. Plus (2018) 133: 289
https://doi.org/10.1140/epjp/i2018-12133-8

Regular Article

Dispersive optical soliton solutions of the higher-order nonlinear Schrödinger dynamical equation via two different methods and its applications

¹ Laboratoire d’Automatique et d’Informatique Appliquée (LAIA), IUT-FV of Bandjoun, The University of Dschang, BP 134, Bandjoun, Cameroon
² Laboratory of Mechanics, Department of Physics, Faculty of Sciences, and African Center of Excellence in I.C.T (C.E.T.I.C), University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon
³ Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
⁴ Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
⁵ Nonlinear Physics and Complex Systems Group, Department of Physics, The Higher Teachers’ Training College, University of Yaounde I, P.O. Box 47, Yaoundé, Cameroon
⁶ Department of Mathematics, Faculty of Science, Jiangsu University, Zhenjian, China

^* e-mail: Aly742001@yahoo.com

Received: 5 May 2018
Accepted: 21 June 2018
Published online: 31 July 2018

Abstract

In this paper, we apply two methods which are the arbitrary nonlinear parameters and the exponential rational function method to construct many new exact solutions of the higher-order nonlinear partial differential equations, namely, the higher-order nonlinear Schrödinger (HNLS) equation. The solutions obtained by the current methods are generalized periodic solutions. The shape of the solutions can be well controlled by adjusting the parameters of the system. Optical soliton solutions obtained can be used to transport information in the telecommunication domain. It also comes from this work that the behavior of this HNLS equation may be easily studied by means of the phase plane plot which is the best tool to predict some solutions.