Solutions of some nonlinear partial differential equations and comparison of their solutions

This study is constructed in seven chapters.In chapter one, some fundamental definitions are given about conservation of laws.In chapter two, nonlinear partial differential equations family that includes the term of are investigated. We analyzed the Boussinesq equation that has an importance place in this family equation.In chapter three, it is made a historical analyze of some methods to obtain analytic 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 four, we studied the flux-density equations that obtained with the aid of conservation of laws of some equations in literature. Especially we obtained the flux-density equations of sixth ordered Boussinesq equation.In chapter five, it is made analyze of a new expansion method and given its applications some nonlinear partial differential equations and some systems. We compared the graphics of solutions which are obtained from -expansion method and -expansion method.In chapter six, it is made a generalized assessment by supporting results which are obtained in this study.