“Good”Boussinesq方程的多辛Fourier拟谱算法

Multisymplectic Fourier Pseudo-Spectral Algorithm for "Good" Boussinesq Equation

对满足周期边界条件的非线性“good”Boussinesq方程作正则变换,得到它的一个多辛方程组及其守恒律.在空间方向用Fourier拟谱方法离散此方程组,然后在时间方向用中点辛格式对半离散方程进行数值求解,得到了非线性“good”Boussinesq方程的多辛Fourier拟谱格式,同时也得到格式的半离散及全离散多辛守恒律.数值实验能很好地模拟原孤立波的运动,验证了所构造格式的有效性与长时间的数值稳定性.

By canonical transformation, multisymplectic systems and multisymplectic conservation laws for nonlinear ＂Good＂ Boussinesq equation with periodic boundary conditions are obtained. Using Fourier pseudo-spectral method in spatial direction and mid-point Euler method in time direction to the multisymplectic systems, a multisymplectic Fourier pseudo-spectral scheme is constructed. At the same time, we have also obtained semi-discrete and full-discrete multisymplectic conservation laws for the scheme. Numerical experiments show that the multisymplectic Fourier pseudo-spectral scheme constructed in this paper is effective, and has excellent long-time numerical behavior.