Eur. Phys. J. Plus (2017) 132: 252
https://doi.org/10.1140/epjp/i2017-11571-0

Regular Article

Some applications of the (G′/G, 1/G)-expansion method to find new exact solutions of NLEEs

¹ Department of Computer Science and Engineering, Southeast University, Dhaka, Bangladesh
² National Institute of Textile Engineering and Research, Dhaka, Bangladesh
³ Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh
⁴ Department of Mathematics, Saint Xavier University, Chicago, USA

^* e-mail: ali_math74@yahoo.com

Received: 19 January 2017
Accepted: 24 April 2017
Published online: 9 June 2017

Abstract

The double (, )-expansion method is an influential, effective and well-suited method to examine closed form traveling wave solutions to nonlinear evolution equations (NLEEs). In this article, we extract abundant wave solutions to the (2+1)-dimensional typical breaking soliton equation and the (1+1)-dimensional classical Boussinesq equation through this method. The wave solutions are presented in terms of hyperbolic function, trigonometric function and rational function. By means of the wave transformation, the NLEEs are reduced to nonlinear ordinary differential equation (ODE) and then the nonlinear ODE is utilized to examine the necessary NLEE. The method can be considered as the generalization of the (-expansion method established by Wang et al. and it is shown that the suggested method is a powerful mathematical tool for investigating nonlinear evolution equations.