On Some Methods Of Solving Exact Solutions To NLPDEs

Under the Homogeneous balance idea, the generalized modified F-expansion method and the extended modified tanh-function method are proposed by taking full advantages of F-expansion method, tanh-function method and Riccati equation in seeking exact solutions of NLPDEs. The method can be conveniently operated with the aid of computer symbolic systems Mathematica, and rich families of exact solutions of NLPDEs have been obtained, including periodic wave solutions, solitary wave solutions, triangle function solutions, rational function solutions, plural number formal solutions, bell-shaped solitary solutions, kink-shape solutions and so on. By using the generalized modified F-expansion method and the extended modified tanh-function method, we have solved the nonlinear dispersive dissipative mKdV equation and the (3+1)-dimensional Burgers equations respectively. 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 under Homogeneous balance idea. As a result, many new and more general exact traveling wave solutions are obtained, such as soliton-like solutions, trigonometric function solutions, exponential solutions and rational solutions, etc.Next, we researched the exact solutions of the nonlinear dispersive dissipative mKdV equation by using a generalized modified F-expansion method. Rich families of exact solutions of them have been obtained, including periodic wave solutions, soliton-like solutions, triangle function solutions, rational function solutions, plural number formal solutions and so on. And some of them are new. We consider these solutions will make sense for explaining some physical phenomenon.Finally, we used the extended modified tanh-function method to solve the (3+1)-dimensional Burgers equations and obtained more rich exact solutions of them, like bell-shaped solitary solutions, kink solutions, soliton-like solutions, plural number formal solutions, rational solutions and so on. This work will be usefull for further research to the equation.