Exact Solutions For Some Nonlinear Partial Differential Equations

With the developing of science and technology, the research for nonlinear problems have run through information science, life science, space science, envi-ronmential science and many other scientific areas. In nonlinear physics and me-chanics, simplified nonlinear evolution equations are often employed to describe the complex nonlinear physics system. The relations between physcial quantities can be revealed by solving the nonlinear equations. Therefore, solving nonlinear equations is a key problem in nonlinear mechanics and physics.The thesis consists of five chapters. In chapter I, containing the development of solving the exact solutions of nonlinear partial equation,the basic theories of the (G’/G,1/G)-expansion method and the research of the thesis. Chapter Ⅱ to Ⅳ are devoted to apply the (G’/G,1/G)-expansion method to solve the MKdV equation with nonuniformity terms, the generalized diffusion model in population problems and the (2 + 1)-dimensional long-short wave equations. we obtain abundant exact trav-eling wave solutions expressed by hyperbolic funtions, the trigonometric funtions and rational functions with parameters. The results indicate that this method is concise and effective when dealing with the variable coefficient partial differential equation and the nonlinear partial differential equations which are complex and have practical significances. Chapter V deals with the nonlinear Derrida-Lebowitz-Speer-Spohn equation. The equation is reduced to a corresponding linear partial differential equation by a nonlinear transformation, then we obtain many exact solutions for the reduced linear partial differential equation by applying the sepa-ration variable method. With the aid of the nonlinear transformation given here,we obtain abundant exact solutions of the Derrida-Lebowitz-Speer-Spohn equa-tion. Finally, the summary of the thesis and the prospect of stduy on the method of solving nonlinear partial differential equations are given.