Lie Symmetry, Simiarity Reduction Of (2+1)-Dimensional Generalized Burgers Equation

At present differential equation is a hot issue in the field of mathematics and physics. Because differential equation is the mathematical model for many physical phenomena, it is very important to reveal the physical phenomena by studying the differential equation. There are many methods to study the differential equation in which the Lie-group method is one of the most important ways.In this paper Lie point symmetries and Lie-B?cklund symmetries for (2+1)-dimensional generalized Burgers equation (u t + u^m u_x + u_xx )_x + u_yy= 0, m∈Z⁺,are obtained by Lie-group method. Using the obtained symmetries, similarity reductions are derived, and some exact solutions are obtained.The main contents of this paper are as follows:Chapter one is an introduction. The background of topics and research status are introduced.Chapter two introduces Lie-group method. In chapter three Lie point symmetries of (2+1)-dimensional generalized Burgers equation are described. Similarity reductions are derived by Lie point symmetries, and some exact solutions are obtained.In chapter four Lie-B?cklund symmetries of (2+1)-dimensional generalized Burgers equation are given. Some new solutions of this equation are obtained.The fifth chapter is summary and prospect.