Some new traveling wave solutions of the modified Benjamin-Bona-Mahony equation via the improved (G/G)-expansion method

Abstract

The improved (G’/G)-expansion method is a powerful mathematical tool for solving nonlinear evolution equations whicharise in mathematical physics, engineering sciences and other technical arena. In this article, we construct some new exact travelingwave solutions for the modified Benjamin-Bona-Mahony equation by applying the improved (G’/G)-expansion method. In themethod, the general solution of the second order linear ordinary differential equation with constant coefficients is used for studyingnonlinear partial differential equations. The solution procedure of this method is executed by algebraic software, such as, Maple. Theobtained solutions including solitary and periodic wave solutions are presented in terms of the hyperbolic function, the trigonometricfunction and the rational forms. It is noteworthy to reveal that some of our solutions are in good agreement with the published resultsfor special cases which certifies our other solutions. Furthermore, the graphical presentations of some solutions are illustrated in thefigures

Keywords

• Traveling wave solutions, the modified Benjamin-Bona-Mahony equation, the improved (G’/G)-expansion method,nonlinear evolution equations

Hasibun Naher1,2, Farah Aini Abdullah2and Ahmet Bekir3

Öz

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