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论文:2012,Vol:30,Issue(6):957-960 |
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引用本文： |
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胡伟鹏, 张宇, 邓子辰. 微扰Landau-Ginzburg-Higgs方程的保结构数值分析[J]. 西北工业大学 |
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Hu Weipeng, Zhang Yu, Deng Zichen. Structure-Preserving Analysis of Perturbed Landau-Ginzburg-Higgs Equation[J]. Northwestern polytechnical university |
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| 微扰Landau-Ginzburg-Higgs方程的保结构数值分析 |
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| 胡伟鹏1,2, 张宇1, 邓子辰1,3 |
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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. 上海交通大学 机械系统与振动国家重点实验室, 上海 200240;
3. 大连理工大学 工业装备结构分析国家重点实验室, 辽宁 大连 116023 |
| 摘要: |
| 基于Hamilton变分原理,构造了微扰Landau-Ginzburg-Higgs方程的一阶广义多辛对称形式,随后对该形式采用多辛差分离散构造其保结构离散格式,最后通过计算机模拟,研究了微扰对Lan-dau-Ginzburg-Higgs方程孤子解的影响,为微扰动力学系统的数值研究提供了新的途径。 |
| 关键词:
有限差分方法
哈密尔顿
孤子解
广义多辛
微扰Landau-Ginzburg-Higgs方程
保结构
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| Structure-Preserving Analysis of Perturbed Landau-Ginzburg-Higgs Equation |
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| Hu Weipeng1,2, Zhang Yu1, Deng Zichen1,3 |
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1. Department of Engineering Mechanics, Northwestern Polytechnincal University, Xi'an 710072, China;
2. State Key Laboratory of Mechanical System & Vibration, Shanghai Jiao Tong University, Shanghai 200240, China;
3. State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, China |
| Abstract: |
| Aim. Perturbation effect,one of the important essential attributes of practical physical and mechanicalsystems,should be reappeared in the structure-preserving analysis process. We now propose the generalized multi-symplectic method to study the perturbation effect of the perturbed Landau-Ginzburg-Higgs equation based on thedeveloping theory of multi-symplecticity. Sections 1 through 3 of the full paper explain our explorative research insome detail. The core of section 1 is that we derive eq. (4) as the generalized multi-symplectic form for the per-turbed Landau-Ginzburg-Higgs equation. The core of section 2 is that we construct the structure-preserving differ-ence scheme eq. (5) for the generalized multi-symplectic form eq. (4). The core of section 3 is that we analyzethe perturbation effect of the perturbed Landau-Ginzburg-Higgs equation system with the generalized multi-symplec-tic method. The results of this paper and their analysis appear to allow studying in a new way the nonconservativetype geometric properties of the Hamilton system. |
| Key words:
finite difference method
Hamiltonians
solitons;generalized multi-symplectic
perturbed Landau-Ginzburg-Higgs equation
structure-preserving
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| 收稿日期: 2011-12-01
修回日期:
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| DOI: |
| 基金项目: 国家自然科学基金(10972182和11002115);111引智计划(B07050);航空科学基金(2010ZB53021);西北工业大学基础研究基金(JC20110259);高校博士点基金(20106102110019);机械系统与振动国家重点实验室开放课题(MSV-2011-21);大连理工大学工业装备结构分析国家重点实验室开放基金(GZ0802)资助 |
| 通讯作者:
Email： |
| 作者简介: 胡伟鹏(1977-)，西北工业大学副教授，主要从事多辛算法在非线性动力学问题中的应用研究。
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| 相关功能 |
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| 作者相关文章 |
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| 胡伟鹏 在本刊中的所有文章 |
| 张宇 在本刊中的所有文章 |
| 邓子辰 在本刊中的所有文章 |
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参考文献: |
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[1] Feng K.On Difference Schemes and Symplectic Geometry.Proceeding of the 1984 Beijing Symposium on D.D.,Beijing: Sci-ence Press, 1984, 42-58
[2] Bridges T J.Multi-Symplectic Structures and Wave Propagation.Mathematical Proceedings of the Cambridge Philosophical Soci-ety, 1997, 121(1):147-190
[3] Bridges T J，Reich S.Multi-Symplectic Integrators: Numerical Schemes for Hamiltonian PDEs That Conserve Symplecticity．Physics Letters A, 2001, 284(4-5):184-193
[4] Hu W P，Deng Z C，Han S M，Fan W.An Implicit Difference Scheme Focusing on the Local Conservation Properties for Bur-gers Equation.International Journal of Computational Methods, 2012, 9(2), 1240028
[5] Hu W P，Han S M，Deng Z C，Fan W.Analyzing Dynamic Response of Nonhomogeneous String Fixed at Both Ends.Interna-tional Journal of Non-Linear Mechanics, 2012, 47(10), 1111-1115
[6] Hu W P，Deng Z C，Han S M，Fan W.Multi-Symplectic Runge-Kutta Methods for Landau-Ginzburg-Higgs Equation.AppliedMathematics and Mechanics-English Edition, 2009, 30(8):1027-1034 |
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