Symmetry Classifications And Reductions Of Several Classes Of Nonlinear Partial Differential Equations

Studying the methods for solving the nonlinear partial differential equations is one of the most advanced contents in the nonlinear physics. One method for solving the nonlinear partial differential equations is Lie symmetry approach. The main research area of partial differential equations with arbitrary parameters is the classifying symmetry, so it is signifi-cance to obtain the symmetry of the nonlinear partial differential equation using Lie group method in the research. It is helpful to acquire its corresponding reduced equation and the exact solutions of the equations,when the type of symmetry of each function is assured. In the article,we discuss the classifying symmetry of several nonlinear partial differential equa-tions and acquire the arbitrary functions of the differential equations, and the corresponding reduced equations.This paper is divided into five chapters as below:The first chapter, introduction part,introduces the present situation and development prospect of partial differential equation. in the meantime, it summarizes the methods of partial differential equations.The second and third chapter discuss the generalized burgers equation ut+f(u)ux-g(u)uxx=0and ut+f(x, u)(ux-uxx)=0using Lie group method. Based on the calculation,we acquire eight types symmetry of f(x, u) and two types symmetry of f(u)、g(u),and obtain the corresponding reduced equation.The forth chapter analyzes the generalized diffusion equation ut=(f(u)ux)y+f(u)ux using Lie group method.The arbitrary function f(u) has been discussed in two situations and calculated the corresponding reduced equation.The fifth chapter summarize the paper and prospect the future work.