The Basic (G'/G)-Expansion Method for the Fourth Order Boussinesq Equation

Hasibun Naher, Farah Aini Abdullah

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia.

DOI: 10.4236/am.2012.310168                

Abstract

The (G'/G)-expansion method is simple and powerful mathematical tool for constructing traveling wave solutions of nonlinear evolution equations which arise in engineering sciences, mathematical physics and real time application fields. In this article, we have obtained exact traveling wave solutions of the nonlinear partial differential equation, namely, the fourth order Boussinesq equation involving parameters via the (G'/G)-expansion method. In this method, the general solution of the second order linear ordinary differential equation with constant coefficients is implemented. Further, the solitons and periodic solutions are described through three different families. In addition, some of obtained solutions are described in the figures with the aid of commercial software Maple.

Keywords

The (G'/G)-Expansion Method; the Fourth Order Boussinesq Equation; Traveling Wave Solutions; Nonlinear Partial Differntial Equations

Conflicts of Interest

The authors declare no conflicts of interest.

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