| 具有单参数空间对称群的向量场及其约化 |
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| 引用本文： | 黄德斌,赵晓华. 具有单参数空间对称群的向量场及其约化[J]. 应用数学和力学, 2000, 21(2): 154-160 |
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| 作者姓名： | 黄德斌 赵晓华 |
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| 作者单位： | 1.中国科学院力学研究所LNM, 北京 100080; |
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| 基金项目： | 国家自然科学基金!资助项目 ( 195 72 0 5 7,19972 0 5 8)，云南省科委应用基础研究基金 |
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| 摘 要： | 对于保持某n-形式的n维向量场,应用Lie群的方法得到结论:当这类向量场有保持n-形式的空间单参数对称群时,可具体地构造出一个与该向量场无关的变换,它不仅使向量场约化掉一维,并且使得约化向量场保持相应的(n-1)-形式.特别,当n=3时,简单地得到了Mezie和Wiggins最近得到的重要结果.
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| 关 键 词： | 向量场 对称群 Lie群 约化 保持n-形式 |
| 收稿时间： | 1997-01-20 |
| 修稿时间： | 1997-01-20 |
The Vector Fields Admitting One-Parameter Spatial Symmetry Group and Their Reduction |
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| Huang Debin,Zhao Xiaohua. The Vector Fields Admitting One-Parameter Spatial Symmetry Group and Their Reduction[J]. Applied Mathematics and Mechanics, 2000, 21(2): 154-160 |
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| Authors: | Huang Debin Zhao Xiaohua |
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| Affiliation: | 1.LNM, Institute of Mechanics, Academia Sinica, Beijing 100080, P. R. China;2.Department of Mathematics, Shanghai University, Shanghai 201800, P. R. China;3.Department of Mathematics, Yunnan University, Kunming 650091, P. R. China |
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| Abstract: | For a n-dimensional vector fields preserving some n-form,the following conclusion is reached by the method of Lie group.That is,if it admits a one-parameter,n-form preserving symmetry group,a transformation independent of the vector field is constructed explicitly,which can reduce not only dimesion of the vector field by one,but also make the reduced vector field preserve the corresponding(n-1)-form.In particular,while n=3,an important result can be directly got which is given by Mezie and Wiggins in 1994. |
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