Landau-Ginzburg-Higgs方程的多辛傅里叶拟谱格式
Multi-symplectic Fourier Pseudospectral Method for the Landau-Ginzburg-Higgs Equation

Landau-Ginzburg-Higgs方程是一个重要的非线性波动方程，应用多辛保结构理论研究了其多辛算法。首先，利用哈密顿变分原理构造了Landau-Ginzburg-Higgs方程的多辛格式；随后，通过空间方向上的傅里叶拟谱离散和时间方向上的辛欧拉离散得到了Landau-Ginzburg-Higgs方程的一种显式多辛离散格式；数值实验模拟了非周期边界的扭状孤立波，结果展示了多辛离散格式的精确性和保持局部守恒量的特性。
In this paper, the multi-symplectic method is used to study an important nonlinear wave equation, named Landau-Ginzburg-Higgs equation. Firstly, the multi-symplectic form of the Landau-Ginzburg-Higgs equation is deduced using the Hamiltonian variational principle. Then, the explicit multi-symplectic discrete scheme is derived by applying the Fourier pseudospectral method to space derivatives and the symplectic Euler method to time derivatives in the multi-symplectic form. The soliton solution with non-periodic boundary is simulated by the proposed scheme. The numerical results show that:the proposed scheme can simulate the soliton solution well and can preserve the local conservation quantities