Implementation Of WTC-Kruskal Algorithm On Mathematica Software

Firstly,this article briefly introduces the research background and current status of Painlevé analysis of ordinary differential equations and partial differential equations based on symbolic calculations;Secondly,for nonlinear evolution equations(partial differential equations),the WTC-Kruskal algorithm for nonlinear evolution equation Painlevé analysis is elaborated.The main steps include the first analysis,finding resonance points and verifying the compatibility conditions;Finally,basing on the Symbol Calculation Mathematica Software,the WTC-Kruskal algorithm is developed into a Painleve Test package that can automatically determine whether the nonlinear evolution equation has Painlevé properties.We provide the detailed code of the package,and also define seven functions,encapsulated in the package Painleve.m,including the Main Function,the Sub-main Function,the Function of Calling the Main Function,the Function of Leading Analysis(leading Analysis),the Function of Verifying Compatibility Conditions(compatibility),the Function of Solving Specific Numerical Order of Equation(leading Exponent)and the Function of Kruska-Painlevé(painleve Kruska).The application scope of this program package is very wide,and high-dimensional or high-order nonlinear evolution equations and systems can be analyzed by Painlevé.The package can also output Painlevé truncated expansion,which is convenient for us to construct the B?cklund transformation and some special forms of exact solutions in the form of human-computer interaction for nonlinear evolution equations,and further study other properties of the equations.