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中文摘要：
非线性波动方程作为一类重要的数学物理方程吸引着众多的研究者，基于Hamihon空间体系的多辛理论研究了Landau—Ginzburg—Higgs方程的多辛算法，讨论了利用Runge—Kutta方法构造离散多辛格式的途径，并构造了一种典型的半隐式的多辛格式，该格式满足多辛守恒律、局部能量守恒律和局部动量守恒律．数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性．
英文摘要：
The nonlinear wave equation, describing many important physical phenomena,has been investigated widely in last several decades. Landau-Ginzburg-Higgs equation, a typical nonlinear wave e- quation, was sdudied based on the multi-symplectic theory in Hamilton space. The multi-symplectic Runge-Kutta method was reviewed and a semi-implicit scheme with certain discrete conservation laws was constructed to solve the first-order partial differential equations that were derived from the Lan- dau-Ginzburg-Higgs equation. The results of numerical experiment for soliton solution of the Landau- Ginzburg-Higgs equation were reported finally, which show that the multi-symplectic Runge-Kutta method is an efficient algorithm with excellent long-time numerical behaviors.
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