A Modified Algorithm Of Differential Form Wu's Method And Its Application In Computation Of Symmetries Of Differential Equations

Theory of differential form Wu's method is a powerful tool in algebra and has widely application. Consequently its application in differential equations problems is expected. The differential characteristic set (Wu's method) for differential polynomial system maintains the essential character of original differential polynomial system. Char-set has triangular form structure,which is used to overcome some difficulties in differential fields problems.In this paper, we study the differential form Wu's method and put emphasis on the algorithm of differential characteristic set for differential polynomial system, and its applications.Firstly, based on the algebra case of Wu's method (T) we give a modified algorithm of differential characteristic set for differential polynomial system - algorithm (T)′.Secondly, we investigate the application of given algorithm in computation of symmetries of differential equations. We calculate the differential characteristic set of determining equations for source evolution equations (include several linear and nonlinear differential system of equations).Finally, we put forward the concept of differential characteristic set modulo with respect to a polynomial and present the properties of the characteristic set.