Symmetry?Conservation Law And Exact Solution Of Several Kinds Of Nonlinear Equations

This paper mainly studies the Riccati equation with variable coefficients,nonlinear dissipative dispersive equation,nonlinear Aceive-dissipative dispersive equation by applying the G'/G-expansion method,Lie group method,power series method.At the same time,new solutions are derived by solving the reduction equations.In chapter 1,the homogeneous balance principle and G'/G method is used for constructing the exact solutions of Riccati equation with variable coefficients.In chapter 2,based on the Lie group method,we find the classical symmetry and reduction.Some exact solutions should be derived by solving the reduce equations,such as power series solution,at last,by using the method of vector field and the adjoint equation obtained generalized nonlinear Aceive dissipation dispersion equation of conservation law..In chapter 3,by applying the direct symmetry method,we get the symmetry of nonlinear dissipative dispersive equation.Based on the compatibility of the symmetry and the nonlinear dissipative dispersive equation,we find some exact solutions of the nonlinear dissipative dispersive equation,which include the G'/G solution,the power series solution and so on..at last,by using the method of vector field and the adjoint equation obtained nonlinear dissipation dispersion equation of conservation law..From what has been discussed above,Lie group method for dimension reduction has great convenience and practicability,By the repeated use of lie group method,finally can reduce the high dimensional equation for one-dimensional ordinary differential equations,For the solution of the differential equation is what we are familiar with,we can through a variety of ways to solve,Such as power series method,the tanh method,the method of auxiliary function,etc.,so that you can get the original high dimensional equation solution.