Eur. Phys. J. Plus (2017) 132: 259
https://doi.org/10.1140/epjp/i2017-11527-4

Regular Article

Solitons and other solutions to nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity using several different techniques

¹ Mathematics Department, Faculty of Sciences, Zagazig University, P. O. Box 44519, Zagazig, Egypt
² Mathematics Department, Faculty of Education and Science, Taiz University, Taiz, Yemen

^* e-mail: alnowehy2010@yahoo.com

Received: 17 March 2017
Accepted: 3 May 2017
Published online: 13 June 2017

Abstract

The -expansion method, the improved Sub-ODE method, the extended auxiliary equation method, the new mapping method and the Jacobi elliptic function method are applied in this paper for finding many new exact solutions including Jacobi elliptic solutions, solitary solutions, singular solitary solutions, trigonometric function solutions and other solutions to the nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity whose balance number is not positive integer. The used methods present a wider applicability for handling the nonlinear partial differential equations. A comparison of our new results with the well-known results is made. Also, we compare our results with each other yielding from these five integration tools.