A Modified F-Expansion Method For Solving Nonlinear PDEs

In this paper, the major contents conclude: under Homogeneous balance idea, a modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of nonlinear PDEs. the method can be conveniently operated with the aid of computer symbolic systems (Mathematica), and rich families of exact solutions of nonlinear PDEs have been obtained, including soliton-like solutions, trigonometric function solutions and rational solutions. By using the method, we have solved Gardner equation, Breaking Soliton Equation, Variant Boussinesq equations and DGH equation with strong dispersive term. Massive exact solutions of them have been obtained, and some of the solutions are new. We also provided some figures of partial solutions for direct-viewing analysis.Firstly, we researched the Backlund transformations and exact solutions of CDG equation by using the homogeneous balance method. Two classes of Backlund transformations for CDG equation are derived and three classes of exact solutions are obtained. Solitary wave solutions belong to these classes. And use these conclusions to expand the solutions of the CDG equation based on original research.Next, we researched the exact solutions of Gardner equation, Breaking Soliton Equation and Variant Boussinesq equations by using a modified F-expansion method, rich families of exact solutions of them have been obtained, including bell-shaped solitary solutions, kink solutions, soliton-like solutions, complex solutions, rational solutions and-so on. And some of them are new. We consider these solutions will make sense for explaining some physical phenomenon.Finally, we researched the exact solutions of DGH equation with strong dispersive term which was recently put forword, and we obtained its kink solutions, soliton-like solutions, complex solutions, rational solutions and so on. These work will be usefull for further research to the equation.