Numerical Solutions Of A Class Of KdV And MKdV Equations With Variable Coefficients By Lie-group Method

KdV equation has many applications in physics and engineering problems as an important class of nonlinear partial differential equation. Lie-group method is a algorithm with preserving the internal structure of differential equations. Nu-merical solutions of KdV equation and mKdV equation with variable coefficients are solved with Lie-group method in this thesis.First, the semi-discrete difference equations on the mainfold Sn-1are ob-tained. Then these matric Lie-group equations are solved by Cayley transforma-tion, and the solution’s norm can be conserved. At last, numerical experiments and numerical results for single soliton and two-soliton solutions are given.