The Exact Solutions Of Nonlinear PDES And A Generalized Modified F-Expasion Method

The major content of this paper is a generalized modified F-expansion method.Under Homogeneous balance idea,the generalized 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 the Kdv-mKdv equation,the(2+1)-dimensional Burgers equations.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 Klein-Gordon equation by using the modified auxiliary method.As a result,many new and more general exact non-traveling wave solutions are obtained including soliton-like solutions, trigonometric function solutions,exponential solutions and rational solutions.Next,we researched the exact solutions of the(2+1)-dimensional Borer-Kaup 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 the Kdv-mKdv equation and the(2+1)-dimensional Burgers equations,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.