Applications of the Sine-Gordon expansion method to the some nonlinear partial differential equations

This study consists four chapters. In the first chapter, we give some fundamental definitions and theorems which are necessary in this study. In chapter two, we present facts of the sine-Gordon Expansion Method. In chapter three, we apply the sine-Gordon Expansion Method to some know nonlinear solution equations, namely; (2+1)-dimensional Zakharov-Kuznetsov equation, Modified Benjamin-Bona-Mahony (mBBM) equation, Equal Width Wave equation, Modified Korteweg–de Vries (mKdV) equation. We obtain new solitary wave solution to the above mentioned models in form of hyperbolic function and trigonometric function solutions. All the computation in this study is carried out with Wolfram Mathematica 9. We verify all the obtained solutions and they indeed all satisfied their corresponding equations, we also plot the two-dimensional and three-dimensional graphics, all with help of Wolfram Mathematica 9. In chapter four the detailed conclusion about the results obtained by sine-Gordon Expansion Method has been given.