Lie Symmetry Analysis And Exact Solutions Of Two Kinds Of The Evolution Equations

In natural and social science field, there are many nonlinear problems which are usually characterized by nonlinear evolution equations. So, the nonlinear evo-lution equations becomes one of the hottest areas in nonlinear science field. and Lie method is one of powerful tools for it. In this thesis, by using Lie group method, we study the Lie classical symmetries and new exact solutions of two kinds of nonlinear evolution equations. including traveling wave solutions,exact power series solutions.In Section one, the Sharma-Tasso-Olver equation is considered. By using the Lie method and with the help of maple or mathematic, we get the Lie clas-sical symmetries, at the same time, adjoint representations, optimal system and the reduced ODEs are obtained. finally, some new group-invariant solutions of STO equation through the generalized G'/G-expansion method are get, including hyperbolic function solutions, triangular function solutions.In Section two, we study the symmetry reductions of the Generalized Kuramoto-Sivashinsky equation. Moreover, we reduce PDE to ODEs, and the exact analytic solutions of the GKS equation are obtained by using the power series method. we can see that these solutions converge quickly. A conclusion is given in the last chapter.