Finding of exact solutions of some partial differantial equations by modified exp (-Ω(ξ))-expansion function method

This study consists of five parts. In the first chapter, a general literature review was performed. It has been given informations on the solution techniques and one the historical structures of partial differential equations was given. In the second chapter, some basic definitions and thereoms which are necessary in this thesis was given. In the third chapter, the general structure of , the modified exp (-Ω(ξ))-expansion function method was given. In the fourth chapter, the modified exp (-Ω(ξ))-expansion function method was applied to KP equation, MQZK equation ,Getmanou equation, Basitleştirilmiş MCH equation, (3+1)-dimensional Jimbo-Miwa equation, KZK equation. New dark soliton, bright soliton, dark-bright soliton, hyperbolic function and trigonometric function solutions of these equations were obtained. Algebraic calculations of these equations were made by using Mathematica 9 program. Two and three dimensional graphs of the new solutions of these equations are drawn with the help of Mathematica 9 program. In the fifth chapter, comprehensive results were given about the new exact solutions obtained in this study.