Determining the exact solutions of some nonlinear partial differential equations by trial equation methods

This study consist of five chapters. In the first chapter, it has been given some informations about the methods, developed for the traveling wave solutions of the nonlinear partial differential equations, and their applications. In chapter two, some fundamental definitions and ideas which are necessary in this thesis study are given. In chapter three, the extended trial equation method, improved tanh function method and new function method are introduced. In chapter four, the traveling wave solutions of the nonlinear partial differential equations are obtained. The generalized Benjamin equation, the generalized Burger-KdV equation, the generalized reduced long wave equation, the Boussinesq equation and the generalized nonlinear Klein-Gordon equation are solved by the extended trial equation method, also (N+1)-dimensional sine-cosine-Gordon, the generalized double sinh-Gordon, (N+1)-dimensional double sine-Gordon, (N+1)-dimensional sinh-cosh-Gordon equations are solved by the new function method, Boussinesq equation are solved by the generalized tanh function method. The graphics of the obtained functions were given in two and three dimensional spaces by using Mathematica program. In chapter five, it has been given a conclusion about techniques used by taking into account analytical, numerical and approximate solutions the methods proposed and used in this thesis study, the solutions found by these methods are evaluated, and the obtained results are given. Key Words: The extended trial equation method, the new function methods, improved tanh function method, the nonlinear partial differential equations, the traveling wave solutions.