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 classifications35C07; 35C08; 35P99
Highlights
The world around us is inherently nonlinear (He 2009) and nonlinear evolution equations (NLEEs) are widely used as models to describe complex physical phenomena in various fields of science and engineering, especially in solid-state physics, plasma physics, fluid mechanics, biology etc
Various methods have been utilized to explore different kinds of solutions of physical problems described by nonlinear evolution equations
In former literature, the solitary wave solutions to the Boussinesq equation have not been studied by this method
Summary
The world around us is inherently nonlinear (He 2009) and nonlinear evolution equations (NLEEs) are widely used as models to describe complex physical phenomena in various fields of science and engineering, especially in solid-state physics, plasma physics, fluid mechanics, biology etc. In recent times, a variety of analytical and semi-analytical methods have been developed and use for solving NLEEs, for instance, the inverse scattering transform (Ablowitz and Clarkson 1991), the complex hyperbolic function method (Chow 1995; Zayed et al 2006), the rank analysis method (Feng 2000), the ansatz method (Hu 2001a, b), The objective of this article is to implement the potential exp(–Ф(η))-expansion method to search solitary wave solutions for nonlinear evolution equations via the fourth order Boussinesq equation. In former literature, the solitary wave solutions to the Boussinesq equation have not been studied by this method
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