Analytical solution of partial differential equations by rational sineGordon expansion method

In this study, sine-Gordon and rational sine-Gordon expansion methods were applied to nonlinear partial differential equations. Especially for Benjamin-Ono equation which has an important place in applied mathematics and partial differential equation systems representing Langmuir and Ion sound waves, the above-mentioned methods were applied and desired solutions were obtained. Apart from these, the solution of the non-linear Hirota and Zoomeron equations were obtained with this rational cine-Gordon method, and the geometric interpretation of the solutions in two and three dimensional space was made. Although it is not easy to reach the solution of these nonlinear equations, the method used here is an effective method. Therefore, the desired solution was easily obtained. In addition, with the help of computer program, geometric interpretation of the solutions in two and three dimensional spaces has been made for some special cases.