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中文摘要：
非线性发展方程由于具有多种形式的解析解而吸引着众多的研究者，借助多辛保结构理论研究了Sine—Gordon方程的多辛算法．利用Hamilton变分原理，构造出了Sine—Gordon方程的多辛格式；采用显辛离散方法得到了leap—frog多辛离散格式，该格式满足多辛守恒律；数值结果表明leap—frog多辛离散格式能够精确地模拟Sine-Gordon方程的孤子解和周期解，模拟结果证实了该离散格式具有良好的数值稳定性．
英文摘要：
The nonlinear wave equation, which possesses various forms of analytical solutions, was investigated widely in last several decades. The multi-symplectic method for the Sine-Gor-don equation in Hamilton space was proposed. Based on Hamiltonian variational principle, the multi-symplectic formulations of the Sine-Gordon equation were deduced, and then, the leap- frog multi-symplectic discretization scheme was constructed using explicit symplectic discrete method. The numerical results for the Sine-Gordon equation illustrate that the leap-frog multi-symplectic scheme can simulate the propagation of the soliton and the periodic solution for the Sine-Gordon equation accurately, which show the superiority of the multi-symplectic algorithm when dealing with nonlinear evolution equations.
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