The Extended F-expansion Method And Study Of Exact Solutions For Some Nonlinear Partial Differential Equations

Seeking exact solutions for partial differential equations has long been a major concert of both mathematicians and physicists. At present, although a number of meth-ods are proposed and developed to look for the exact solutions of nonlinear partial differential equations, unfortunately, not all these approaches are universally applica-ble for solving all kinds of nonlinear partial equations directly. As a consequence, it is still a very significant task to go on searching for various powerful and efficient approaches to solve nonlinear partial differential equations.In this thesis, we have carried on an introduction to the established thought of F-expansion method and its promotion in detail. By making use of this approach, a variety of exact solutions to some physically significant nonlinear partial differential equations are easily presented. Among them, some are in very good agreement with those obtained in some literatures, others are new ones which can not be found in the existing literatures to the best of our knowledge. This method enriched and improved the content about the exact solution study of nonlinear partial differential equations.The thesis consists of five chapters in total. In chapter one, we have briefly reviewed the historical background of soliton. The main external or internal methods for solving of nonlinear partial differential equations are summarized and the point aim of research and the primary contents of this thesis are also reported.In chapter two, the F-expansion method and its application operating process have been elaborated in detail.In chapter three, the F-expansion method has been applied to explore the exact solutions to Double nonlinear and Double dispersion dominant equation, obtaining some new periodic wave solutions and Jacobi elliptic solutions.In chapter four, we have futher using the F-expansion method to have solved the long and short wave resonance equation. We can also obtain some new periodic wave solutions and Jacobi elliptic solutions.In chapter five, we have adopted the F-expansion method to still obtain some new periodic wave solutions and Jacobi elliptic solutions to the Schrodinger equation Finally, we have provided conclusions of this thesis and have looked ahead of research orientation in future as well.