Determination And Application Of Symmetric Properties Of Partial Differential Equation Based On Mechanization Method

In this thesis,a summarized process of solving partial differential equations with classical symmetry is given and some related Lie algebra knowledge is described.A application of the Killing form of Lie algebra to the property of Lie algebra has been introduced in this paper and gives its specific algorithm.The application of Lie symmetry in the study of parabolic equations and 1+2-BK equations is described in detail:By Lie symmetry method and mechanized algorithm,the determination of lie algebraic property of parabolic equation and its application in the optimization system are given;The optimization system of Lie algebra for the 1+2 dimensional parabolic equations is given,and the results of 1+ 1 dimension are promoted;The reduction of the 1+2-BK equation is given,and the equations are transformed into ordinary differential equations under the premise of preserving the invariant solution,which can be easily obtained by the exact solution of the equation.