Traveling Wave Solutions of the Fourth Order Boussinesq Equation via the Improved (G'/G) Expansion Method

Abstract

In this article, the fourth order Boussinesq equation is investigated to generate many new traveling wave solutions via the improved (G'/G) -expansion method. In the method the second order linear ordinary differential equation with constant coefficients is used. Also, the resulted solutions are presented in three different families including solitons and periodic solutions. Furthermore, some of our solutions are coincided with published results which gained by other authors and some are new. Aims: The aim of this work is to construct many new exact traveling wave solutions including solitons, periodic and rational solutions of the fourth order Boussinesq equation by applying the improved  (G'/G)-expansion method. Methodology: The improved  (G'/G)-expansion method is effective and powerful mathematical tool for solving nonlinear partial differential equations which arise in mathematical physics, engineering sciences and other technical arena. In addition,  together with , is implemented as traveling wave solutions, where either  or  may be zero, but both  and  cannot be zero at the same time. Results: The obtained traveling wave solutions are described in terms of the hyperbolic functions, the trigonometric functions and the rational functions. Conclusion: The constructed solutions may express a variety of new features of waves, further, may be valuable in the theoretical and numerical studies of the considered equation. Moreover, the obtained exact solutions reveal that the improved -expansion method is a promising mathematical tool, because, it can establish abundant new traveling wave solutions of different physical structures. Also, some of our solutions are in good agreement with already published results for a special case and others are new.