Periodic wave solutions of some nonlinear partial differential equations

This study is constructed in seven chapters.In chapter one, some fundamental definitions are given.In chapter two, it is made a historical analyze of some methods to obtain periodic wave solutions of nonlinear partial differential equations. All of these methods are based on finding balance term with balancing of the highest order linear and nonlinear term. So, these methods can be only applied to nonlinear partial differential equation. Moreover, these methods convert a nonlinear partial differential equation to an ordinary differential equation. Therefore, solution can be obtained easily.In chapter three, it is obtained periodic solutions of some nonlinear partial differential equations by using one of the methods whose analysis is made in chapter two.In chapter four, it is made analyze of some semi analytical methods which are used to solve linear and nonlinear equations.In chapter five, it is obtained series solutions for equations which are considered in third chapter by using semi analytical methods whose analysis are made in chapter four.In chapter six, it is discussed numerical results of series solutions which are obtained in chapter five.In chapter seven, it is made a generalized assessment by supporting results which are obtained in this study with some studies in literature.Keywords: Solitary waves, Solitons, Jacobi elliptic function, Balance term, Analytical solution, Periodic solution, Tanh method, Jacobi elliptic function method, -expansion method, Exp-function method, SRLW equation, (1+1) dimensional dispersive long wave equation, Semi analytical methods, Series solution, Adomian decomposition method, Homotopy analysis method, Homotopy perturbation method.