Algorithem Research To Obtain Symmetry Group For Two Types Of Soliton Equations Based On Symbolic Compution

In the paper we derived symmetry groups and algorithm of two types solition equations based on soymbolic computation. In the paper we research difference differential equations and no-lieanr partial differential equations respectively,aiming to derive the full symmetry groups of the given differential equations and summrise the procedure of algorithm.The symmetry group direct method is extended to investigate Lie symmetry groups of two differential-difference equations based on the symbolic computation software in the second charpter. Through analysis and tedious calculation, the full symmetry groups of the well-known D?-KP equation and Toda lattice equation are obtained. From them, both the Lie point symmetry groups and a group of discrete transformations can be obtained. In addition, the equvilation of the derived result and the result drawed form Lie symmetry method indicates that it is absolutely correct. Furthermore, based on the full symmetry groups and some simple solutions of these two equations, some general solutions are constructed.In the third charpter employing the symmetry group direct method and symbolic computation software to draw the full symmetry group of the complicated partial differential equations KP-B and BKK. Both the Lie point groups and the non-Lie symmetry group of the nonisospectral KP-B and BKK are obtained. Then some exact solutions of the two equations are derived from two simple travelling wavef solutions by the finite symmetry transformation groups.Direct method was successfully extended to investigate two kinds differential equations through reseach for the full symmetry groups. And the algorithm to obtain the symmetry groups of differential equations was given. In this letter proves the correctness of the method and constructs the more practical general solutions. The result which was obtained via the extended direct method is more simple and understandable and also important to the reseach of soliton theory. What's more, it is valuable to promote the given algorithm for the reseach of differential equations.