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论文:2016,Vol:34,Issue(6):1011-1015 |
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引用本文： |
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张宇, 邓子辰, 胡伟鹏, 杨小锋. Landau-Ginzburg-Higgs方程的多辛傅里叶拟谱格式[J]. 西北工业大学学报 |
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Zhang Yu, Deng Zichen, Hu Weipeng, Yang Xiaofeng. Multi-symplectic Fourier Pseudospectral Method for the Landau-Ginzburg-Higgs Equation[J]. Northwestern polytechnical university |
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| Landau-Ginzburg-Higgs方程的多辛傅里叶拟谱格式 |
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| 张宇1, 邓子辰1, 胡伟鹏1, 杨小锋2 |
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1. 西北工业大学 力学与土木建筑学院, 陕西 西安 710072;
2. 西北农林科技大学 理学院, 陕西 杨凌 712100 |
| 摘要: |
| 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。 |
| 关键词:
Landau-Ginzburg-Higgs方程
多辛积分
傅里叶拟谱方法
孤立波
局部守恒律
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| Multi-symplectic Fourier Pseudospectral Method for the Landau-Ginzburg-Higgs Equation |
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| Zhang Yu1, Deng Zichen1, Hu Weipeng1, Yang Xiaofeng2 |
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1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, China;
2. College of Science, Northwest A & F University, Yangling 712100, China |
| Abstract: |
| 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. |
| Key words:
Landau-Ginzburg-Higgs equation
multi-symplectic integrator
Fourier pseudospectral method
solitary wave
local conservation laws
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| 收稿日期: 2016-03-20
修回日期:
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| DOI: |
| 基金项目: 国家自然科学基金（11372252）资助 |
| 通讯作者:
Email： |
| 作者简介: 张宇(1988-),西北工业大学博士研究生,主要从事多辛方法在动力学中的应用研究。
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