二维非定常Sine-Gordon方程辛算法及其孤子数值模拟

Symplectic Algorithm and Simulation of Solitons for Two-dimensional Non-stationary Sine-Gordon Equation

在矩形域[-a,a]×[-a,a]内对微分算子L=2x2+2y2用5点差分格式将二维非定常Sine Gordon方程离散化为一个2×7992阶非线性Hamilton系统.对该系统使用Euler中心格式,得到一个非线性方程组.对此方程组建立迭代解法并给出了这个迭代方法的收敛条件和收敛速度.Sine Gordon方程单孤子和双孤子的数值模拟试验显示该辛算法是有效的.

A 2×799\+2\|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=\+2x\+2+\+2y\+2 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.