Based On The Auxiliary Equation Method Of Solving Fractional Order Nonlinear Partial Differential Equations

With the continuous development and application of computer technology,as well as the further improvement of the theory of nonlinear science,the exact solution of nonlinear partial differential equations has become a significant research work.Many scholars are committed to solving fractional order nonlinear partial differential equation,therefore,the solution of fractional order nonlinear partial differential equations has become a research topic.At present,there are many methods can solve the exact solutions of fractional nonlinear partial differential equations,such as homogeneous balance method,B?cklund transform method and so on.This article mainly on the basis of previous studies,further research of B?cklund transform and applications of nonlinear superposition formula to nonlinear partial differential equations by using the auxiliary equation well,calculate the various forms fractional order nonlinear partial differential equation infinite sequence solutions.This paper made a lot of research and description of fractional order nonlinear partial differential equations,as follows: the first chapter describes the theory of nonlinear science,research and development of the soliton,brief introduction of methods used for fractional partial differential equations and the research and development of research.The second chapter studies using Riccati equation as the auxiliary equation research the time-space fractional equation nonlinear partial differential equation PKP equation and Gardner equation.The third chapter studied respectively by the Riccati equation and the first auxiliary elliptic equation study time-space equation of fractional order nonlinear partial differential equation m BBM equation and analysis the advantages and disadvantages of the two auxiliary equation.The fourth chapter summarizes the full text,and the content of the article.