| Benney方程的对称和群不变解 |
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| 引用本文： | 陈玮玮.Benney方程的对称和群不变解[J].南京工业大学学报(自然科学版),2006,28(2):89-91. |
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| 作者姓名： | 陈玮玮 |
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| 作者单位： | 南京工业大学,理学院,江苏南京,210009 |
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| 摘 要： | 主要讨论Benney方程的一些对称以及与这些对称相应的单参数不变群的群不变解。Benney方程直接求解较困难．这里将其某些类型的求解转化为常微分方程，首先讨论了Benney方程的一些对称及其李代数，接着给出了与这些对称相应的单参数不变群，然后利用对称约化给出Benney方程的相应于这些单参数不变群的群不变解。对于Benney方程这一不易直接求解的高阶偏微分方程，文章利用了对称约化这种与微分几何密切相关的方法，给出了其一些特殊的解。
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| 关 键 词： | Benney方程 对称 单参数不变群 群不变解 |
| 文章编号： | 1671-7643(2006)02-0089-03 |
| 收稿时间： | 2005-04-29 |
| 修稿时间： | 2005年4月29日 |
Symmetries and group-invariant solutions of the Benney equation |
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| CHEN Wei-wei.Symmetries and group-invariant solutions of the Benney equation[J].Journal of Nanjing University of Technology,2006,28(2):89-91. |
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| Authors: | CHEN Wei-wei |
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| Institution: | College of Sciences, Nanjing University of Technology, Nanjing 210009, China |
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| Abstract: | Some symmetries and group-invariant solutions of Benney equation were discussed. Usually, it is difficult to obtain solutions of Benney equation directly and the usual way is to seek solutions through some ordinary differential equations . And the solutions of these ordinary differential equations are special solutions to Benney equation. Firstly, this paper concerns some symmetries of Benney equation and their Lie algebra. Then according to these symmetries it gives some one-parameter invariant group. At last, it utilizes symmetry reductions to obtain some group-invariant solutions of Benney equation. |
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| Keywords: | Benney equation symmetry group-invariant solution one-parameter invariant group |
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