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International Journal of Mathematical Research

January 2016, Volume 5, 1, pp 63-74

The (F/G)-Expansion Method and Travelling Wave Solutions of Nonlinear Evolution Equations

Ä°brahim Celik

Ä°brahim Celik 1

  1. Faculty of Arts and Sciences, Department of Mathematics, Pamukkale University, Denizli, Turkey 1

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Pages: 63-74

DOI: 10.18488/journal.24/2016.5.1/24.1.63.74

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Abstract:

The (F/G)-expansion method is firstly proposed, where F=F(ξ) and  G = G(ξ) satisfies a first order ordinary differential equation systems (ODEs). We give the exact travelling wave solutions of the variant Boussinesq equations and the KdV equation and by using (F/G)-expansion method. When some parameters of present method are taken as special values, results of the  -expansion method are also derived. Hence,  -expansion method is sub method of the proposed method. The travelling wave solutions are expressed by three types of functions, which are called the trigonometric functions, the rational functions, and the hyperbolic functions. The present method is direct, short, elementary and effective, and is used for many other nonlinear evolution equations.

Contribution/ Originality
This study contributes in the existing literature of  -expansion method. We proposed the (F/G)-expansion method and investigated the exact travelling wave solutions of the variant Boussinesq equations and the KdV equation by using (F/G)-expansion method.

Keywords:

Nonlinear, (F/G)- expansion, Homogeneous balance, Travelling wave, KdV equation, Variant Boussinesq.

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