Group Analysis Of Generalized Caudrey-Dodd-Gibbon Equation And Benney Equation With Variable Coefficients

The nonlinear science is widely applied in nature sciences, such as biology, physics, chemistry, medical science, economics and so on. The nonlinear system which emerges in these disciplines makes the research of nonlinear equations and exact solutions particularly important. And because the existence of symmetries and conservation laws, symmetry research has become an important topic.In this paper, we directly use classic lie group method to discuss optimal systems, reduction equations and exact solutions of two kinds of evolution equa-tions. First, we study the classical symmetries of generalized Caudrey-Dodd-Gibbon(CDG) equation by classical Lie group method, getting the invariant groups and optimal systems. We directly seek for exact solutions of generalized CDG equation by (G'/G)-expansion method. Second, we discuss group analysis of Ben-ney equation with variable coefficients. We get the optimal systems and the re-duced equations of it. By solving the character equations and the invariants, eventually some exact solutions of it in some cases are obtained. Finally, we give a summery of this paper.