Eur. Phys. J. Plus (2019) 134: 159
https://doi.org/10.1140/epjp/i2019-12545-x

Regular Article

Extension of rational sine-cosine and rational sinh-cosh techniques to extract solutions for the perturbed NLSE with Kerr law nonlinearity

Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, 54590, Lahore, Pakistan

^* e-mail: toghazala2003@yahoo.com

Received: 9 October 2018
Accepted: 9 January 2019
Published online: 16 April 2019

Abstract

In this paper, we present the extension of the rational sine-cosine method and rational sinh-cosh method to construct the new exact solutions of a nonlinear evolution equation that appears in mathematical physics, specifically the perturbed nonlinear Schrödinger equation (NLSE) with Kerr law nonlinearity. As a result, trigonometric, hyperbolic and complex function solutions in the form of solitons and periodic wave solutions are characterized with some free parameters of the problem studied. The obtained results demonstrate that the proposed techniques are the significant addition for exploring various types of nonlinear partial differential equations (PDEs) in applied sciences. Moreover, graphical representations and physical explanations of some chosen exact solutions are plotted to describe the propagations of traveling wave solutions.