| An important branch of the partial differential equations are nonlinear par-tial differential equations, and the exact solution of nonlinear partial differential equation and its solution is a key element of Nonlinear Science. The exact solu-tion of nonlinear partial differential equation and its solution as a cutting-edge research topics and hot issues in nonlinear science challenging. Present, although has been proposed and developed the exact solution of nonlinear partial differen-tial equations method for solving nonlinear partial differential equations there is no unified and universal approach, continue to find effective and feasible method is still a very important and valuable work.Nonlinear science is a basic science study of nonlinear phenomena in com-mon. It is a comprehensive discipline,since the1960s, it gradually devel-oped,based on the branches of nonlinear subdisciplines. Nonlinear Science, in-volving almost all fields of natural sciences and social sciences, is changing the traditional view of social reality,it is known as the "third revolution" of natural sciences in the20th century.In this paper,we use the two kinds of expansion methods to con-struct the traveling wave solutions of nonlinear partial differential equations. First,Thel/G’ expansion method combined with the homogeneous balance prin-ciple is used for solving the Chaffee-Infante reaction diffusion equation. The solitary wave solutions of the equation are obtained. Second, Combined with homogeneous balance method, we use the G/G’ expansion method to construct traveling wave solutions of Landau-Ginzburg-Higgs equation and fifth-order dif-fusion equation. By Maple soft, we obtained some traveling wave solutions ex-pressed by hyperbolic functions, the trigonometric functions and rational func- tions. Seen from the solution process,this method is simple, direct and basic in solving high order nonlinear partial differential equations. |
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