Abstract: A 2×799²-order nonlinear Hamiltonian system of two-dimensional non-stationary Sine-Gordon equation is introduced when the five point difference scheme is used to discretize the differential operator L=(ə²)/(əx²)+(ə²)/(əy²) in the rectangle [-a,a]×[-a,a]. An iterative method is designed to solve the nonlinear system, which is formed by using the centered Euler scheme for the Hamiltonian system. The condition and the velocity of convergence for this method are given. Numerical examples for evaluating one-soliton and two-soliton of the Sine-Gordon equation show that the symplectic method is an efficient algorithm.

Key words: Sine-Gordon equation, Hamiltonian system, symplectic scheme, soliton