Eur. Phys. J. Plus (2019) 134: 506
https://doi.org/10.1140/epjp/i2019-13037-9

Regular Article

A novel technique to construct exact solutions for nonlinear partial differential equations

¹ Department of Engineering Science, Kermanshah University of Technology, Kermanshah, Iran
² Department of Mathematics, Faculty of Engineering and Natural Sciences, Bahcesehir University, 34349, Istanbul, Turkey
³ Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey
⁴ Institute of Space Sciences, Magurele-Bucharest, P.O.Box, R 76900, MG-23, Romania

^* e-mail: dumitru@cankaya.edu.tr

Received: 28 April 2019
Accepted: 2 July 2019
Published online: 14 October 2019

Abstract

The aim of the manuscript is to present a new exact solver of nonlinear partial differential equations. The proposed technique is developed by extending the -model expansion method as a known method. The corresponding exact solutions are given in terms of Jacobi elliptic functions. Some new optical solutions of the resonant nonlinear Schrödinger equation are constructed within this newly proposed method. For some specific choices of the modulus of Jacobi elliptic functions, various solutions of the equation are introduced. Some numerical simulations are also included to emphasize that all parameters have major influences for the solitary waves behaviours. The proposed technique is very simple and straightforward, and can be employed to solve other non-linear partial differential equations.