| In this paper, the major contents conclude: under Homogeneous balance idea, by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of nonlinear PDEs, a modified F-expansion method is used solving the coupled Schrodinger-Boussinesq equations and the dispersive dissipative equation. Simultaneously we proposed a generalized modified F-expansion method. 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 coupled MKdV 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 exact solutions of the dispersive dissipative equation by using the modified F-expansion method. Several classes of exact solutions for the dispersive dissipative equation are obtained. Solitary wave solutions belong to these classes. By using Mathematica some figures of partial solutions are provided for direct-viewing analysis.Next, we researched the exact solutions of coupled Schrodinger-Boussinesq equations by using the 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 introduced a generalized modified F-expansion method and researched the exact solutions of the coupled MKdV equations. we obtained its kink solutions, soliton-like solutions, complex solutions, rational solutions and so on. This work will be useful for further research to the equation.
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