Study On Exact Solutions Of Several Nonlinear Partial Differential Equations

With the more and more extensive research fields of nonlinear science,the study of nonlinear phenomena found in the real world is more and more in-depth.Because the exact solutions of nonlinear partial differential equations can explain the nonlinear phenomena,the exact solutions of nonlinear partial differential equations are always the focus of nonlinear science research.Many effective methods for solving nonlinear partial differential equations have been proposed by relevant scholars,but these methods are only effective for some nonlinear partial differential equations,and there is no unified solution method and theory at present.For nonlinear partial differential equations,it is necessary to continuously explore new solutions and improve the existing solutions.In this paper,we mainly study the construction of exact solutions of several nonlinear partial differential equations.Firstly,the research background and significance of the exact solutions of nonlinear partial differential equations are described,and the development of the methods for solving nonlinear partial differential equations is briefly described.Secondly,the concept of nonlinear partial differential equation is given and several common solving methods are introduced.Then,using the generalized tanh function expansion method and the new solution of Riccati equation,the Benjamin-Ono equation and the generalized Zakharov-Kuznetsov equation are solved based on the traveling wave transformation,and the new exact traveling wave solutions are obtained,which enrich the solution system.Finally,by using the generalized Riccati equation mapping method,the(2+1)-dimensional Boiti-Leon-Pempinelli equation with variable coefficients,the(2+1)-dimensional Broer-Kaup-Kupershmidt equation with variable coefficients,and the(3+1)-dimensional Jimbo-Miwa equation are solved,and a large number of accurate solutions of nontraveling waves are obtained.It fully demonstrates the effectiveness and practicability of the generalized tanh function expansion method and the generalized Riccati equation mapping method,it also illustrates the important application of the hypothetical idea of understanding in the solution of nonlinear partial differential equations.