| 耦合Burgers系统的Painlevé性质分析，对称和对称约化 |
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| 引用本文： | 连增菊,陈黎丽,楼森岳.耦合Burgers系统的Painlevé性质分析，对称和对称约化[J].中国物理 B,2005,14(8):1486-1494. |
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| 作者姓名： | 连增菊 陈黎丽 楼森岳 |
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| 作者单位： | Center of Nonlinear Science and Department of Physics, Ningbo University, Ningbo 315211, China;Center of Nonlinear Science and Department of Physics, Ningbo University, Ningbo 315211, China ;Department of Physics, Shanghai Jiaotong University,Shanghai 200030, China;Center of Nonlinear Science and Department of Physics, Ningbo University, Ningbo 315211, China ;Department of Physics, Shanghai Jiaotong University,Shanghai 200030, China |
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| 基金项目： | Project supported by the National Natural Science Foundations of China (Grant Nos 90203001 and 10475055) and the Scientific Research Fund of Zhejiang Provincial Education Department (Grant No 20040969). |
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| 摘 要： | 本文给出了耦合Burgers系统的Painlevé性质，逆强对称算子，无穷多对称和李对称约化。通过把强对称和逆强对称算子重复多次作用到耦合Burgers模型的一些平庸对称，如恒等变换，空间平移变换和标度变换上，我们得到了三族无穷多对称。这些对称构成了无穷维李代数。用其中的有限维子代数——点李代数对模型进行对称约化，得到了模型的群不变解。
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| 关 键 词： | 对称，强对称，对称约化，Painlevé分析。 |
| 收稿时间： | 2004-12-19 |
Painlevé property, symmetries and symmetry reductions of the coupled Burgers system |
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| Lian Zeng-Ju,Chen Li-Li and Lou Sen-Yue.Painlevé property, symmetries and symmetry reductions of the coupled Burgers system[J].Chinese Physics B,2005,14(8):1486-1494. |
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| Authors: | Lian Zeng-Ju Chen Li-Li and Lou Sen-Yue |
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| Institution: | Center of Nonlinear Science and Department of Physics, Ningbo University, Ningbo 315211, China; Center of Nonlinear Science and Department of Physics, Ningbo University, Ningbo 315211, China ;Department of Physics, Shanghai Jiaotong University,Shanghai 200030, China; Center of Nonlinear Science and Department of Physics, Ningbo University, Ningbo 315211, China ;Department of Physics, Shanghai Jiaotong University,Shanghai 200030, China |
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| Abstract: | The Painlev\'e property, inverse recursion operator,infinite number of symmetries and Lie symmetry reductions of the coupled Burgers equation are given explicitly. Three sets of infinitely many
symmetries of the considered model are obtained by acting the recursion operator and the inverse recursion operator on the trivial symmetries such as the identity transformation, the space translation and the scaling transformation respectively. These symmetries constitute an infinite dimensional Lie algebra while its finite dimensional Lie point symmetry subalgebra is used to find possible symmetry reductions and then the group invariant solutions. |
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| Keywords: | symmetry recursion operator symmetry reduction Painlevé |
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