Solitary wave solutions of the fourth order Boussinesq equation through the exp(-Ф(η))-expansion method

M Ali Akbar; Norhashidah Hj Mohd Ali

doi:10.1186/2193-1801-3-344

Solitary wave solutions of the fourth order Boussinesq equation through the exp(-Ф(η))-expansion method

Springerplus. 2014 Jul 8:3:344. doi: 10.1186/2193-1801-3-344. eCollection 2014.

Authors

M Ali Akbar¹, Norhashidah Hj Mohd Ali²

Affiliations

¹ Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh.
² School of Mathematical Sciences, Universiti Sains Malaysia, Pulau Pinang, Malaysia.

Abstract

Abstract: The exp(-Ф(η))-expansion method is an ascending method for obtaining exact and solitary wave solutions for nonlinear evolution equations. In this article, we implement the exp(-Ф(η))-expansion method to build solitary wave solutions to the fourth order Boussinesq equation. The procedure is simple, direct and useful with the help of computer algebra. By using this method, we obtain solitary wave solutions in terms of the hyperbolic functions, the trigonometric functions and elementary functions. The results show that the exp(-Ф(η))-expansion method is straightforward and effective mathematical tool for the treatment of nonlinear evolution equations in mathematical physics and engineering.

Mathematics subject classifications: 35C07; 35C08; 35P99.

Keywords: Fourth order Boussinesq equation; Solitary wave solutions; Soliton; Traveling wave solutions; exp(–Ф(η))-expansion method.