A Class Of Nonlinear Partial Differential Equations Of Painlev(?) Analysis

In recent years,with the continuous development and progress of science and technology,whatever both society and life has rapidly changed.However,the development of society and life and progress is inseparable from the continuous innovation and progress of science and technology.In this age of information,Mathematics plays a key role to the development of science and technology.Especially math becomes even more important in the field of nonlinear science,because of a lot of phenomenon in nature,society is nonlinear,So that prompt in nonlinear science becomes academic research object.From September 1844,Russell at the British association for the advancement of science's 14 th meeting in "wave theory" for the first time proposed the solitary wave phenomenon,the nonlinear science research is pulled open heavy curtain.Later in the study,the scientists novel found many nonlinear partial differential equation,but to solve the exact solutions of nonlinear partial differential equation of the problem,has become the problem that the scientists are now facing it once again.Because there is no system and unified method to solve the nonlinear partial differential equation for accurate solution,scientists can only on the basis of their understanding,think a lot of solutions.Painlev(?) method is presented in this paper is on the basis of predecessors' research,discussing the Painlev(?) property of several nonlinear partial differential equation,in order to provide a preliminary judgment for exact solutions of nonlinear partial differential equation.The article are mainly divided into four parts:The first part: the preliminary knowledge.This section introduces the nonlinear partial differential equation,Painlev(?)property of historical background,research status and innovation points;Presents a nonlinear partial differential equation and the basic concept of Painlev(?),lemma and results.Including: Painlev(?) property,the WTC method,the nonlinear partial differential equation with variable coefficients,etc.The second part: the introduction of Painlev(?) property.In this part mainly introduce the main methods in this paper,we study the WTC method,which is an important way to judge of nonlinear partial differential equation,and introduces the main steps of the WTC method.The third part: comparing a few kinds Painlev(?) property of partial differential equations.This part is the main content of this article,which mainly introduces the WTC method to judge whether such RLW—Burgers equation and Burgers-KdV equation have Painlev(?) property or not.The fourth part of this paper summarizes the work and looks forward to the latest research.