The Exact Solutions Of Generalized DS Equation With Arbitrary Power Nonlinear And Zakharov Equation

In modern mathematics,nonlinear partial differential equations play an im-portant role in the practical application and theoretical study.In recent years,many scholars have studied some nonlinear partial differential equations.How-ever,there are still a large number of solutions to nonlinear partial differential equations that are not solved.And there is no uniform method for solving nonlin-ear partial differential equations.Then,in order to find an effective and feasible method,it becomes a significant and far-reaching research.In this thesis,applying the(G'/G,1/G)-expansion method and the novel(G'/G)-expansion method solves generalized Davey-Stewartson equations with arbitrary power nonlinearities and generalized Zakharov equations with arbitrary power nonlinearities for obtaining some exact solutions.Furthermore,it also expands the solutions of these two equations.First,using the(G'/G,1/G)-expansion method solves the equations.We need to consider a row-wave transformation first.Then,it converts the partial differential equations into an ordinary differential equations,which is equivalent to the planar dynamic system.Combining the ordinary dif-ferential qualitative theory with the maple software,it can get the exact solutions of the equations.Secondly,applying the novel(G'/G)-expansion method researchs these equations.In addition,we consider the traveling wave transform and the cole-hopf transform.Then,by balancing the higher-order nonlinear term and the higher-order linear term,it can determine the positive integer n.Finally,the exact solutions of the equations can be obtained by the maple software.What's more,by comparing the results obtained in this thesis with the results obtained by the previous ones,it can be proved that the results of this paper are new.In this work,it finally gets the kink wave solutions,solitary wave solutions,anti-kink wave solutions and periodic wave solutions,which can be represented by functions,such as exponential functions,trigonometric functions,hyperbolic functions and Jacobian elliptic functions.The results obtained by the(G'/G,1/G)expansion method and the novel(G'/G)expansion method are more rich.At the same time,it also shows that these two methods are very effective and direct for solving nonlinear partial differential equations.