The Exact Solution Of Two Types Nonlinear Evolution Equations Via The Extended(G'/G)-expansion Method

For a long time,seeking solutions(the exact solution and numerical solution)of equations is an important research topic in the field of partial differential equations.In order to reveal the inherent law of some problems in natural sciences,people often set up the corresponding nonlinear evolution equation(s)and find its exact solutions,then we can have a further understanding for the law of internal mechanism by the research on the property of the solutions.Therefore,the theoretical research and calculating the exact solutions for nonlinear evolution equations plays a significant role and attracts more and more experts and scholars' attention.In recent years,here comes many effective methods to solve the nonlinear evolution equations,such as the homogeneous balance method,the hyperbolic function method,the Riccati function method and the (G'/G)-expansion method and so on.In particular,the (G'/G))-expansion method proposed by Wang in 2008,is widely applied in solving nonlinear evolution equations.On the basis of the (G'/G)-expansion method,many scholars did an in-depth research and promotion and obtained a large number of outstanding achievements.Firstly,this article introduces the (G'/G)-expansion method,the generalized (G'/G)-expansion method and the (G'/(G'+G))-expansion method to solve nonlinear evolution equations in detail.Then the generalized (G'/G)-expansion method and the (G'/(G'+G))-expansion method are employed to solve (2+1)-dimensional ANNV system (?) and KPP equation (?) respectively.Compared with the solution obtained by the original method,it is not hard to find that exact solution in new forms,including hyperbolic function,trigonometric function solutions and rational function,is obtained,which enriches the solutions system.Therefore,the generalized (G'/G)-expansion method and (G'/(G'+G))-expansion method in solving nonlinear evolution equations is full of research value.