Multi-Symplectic Leap-Frog Scheme for Sine-Gordon Equation
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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.
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关键词:
- 保结构 /
- 多辛方法 /
- sine-Gordon方程 /
- leap-frog格式
Abstract: The nonlinear wave equation, which possesses various forms of analytical solutions, has been investigated widely in last several decades. The multi-symplectic method for the sine-Gordon 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 sineGordon equation accurately, which show the superiority of the multi-symplectic algorithm when dealing with nonlinear evolution equations.-
Key words:
- structure-preserving /
- multi-symplectic method /
- sine-Gordon equation /
- leap-frog scheme
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