| 李群方法对一阶偏微分方程的应用 |
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| 引用本文： | 刘胜,管克英. 李群方法对一阶偏微分方程的应用[J]. 数学研究及应用, 2000, 20(4): 545-549 |
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| 作者姓名： | 刘胜 管克英 |
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| 作者单位： | 1. 石油大学基础系,北京,102200
2. 北方交通大学数学系,北京,100044 |
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| 摘 要： | 本文以李群为工具，给出了一种将一阶非线性偏微分方程化简为一阶拟线性方程或可积的一阶拟线性方程的方法.该方法可用于某些两个自变元的，接受一个或两个李群的一阶非线性偏微分方程，特别可用于某些单自由度Lagrange系统的Hamilton-Jacobi方程的求解.
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| 关 键 词： | 李群； 一阶偏微分方程； Hamilton-Jacobi方程； 可积性. |
| 收稿时间： | 1997-09-15 |
The Application of Lie Group Method to First Order Partial Differential Equations |
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| LIU Sheng and GUAN Ke-ying. The Application of Lie Group Method to First Order Partial Differential Equations[J]. Journal of Mathematical Research with Applications, 2000, 20(4): 545-549 |
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| Authors: | LIU Sheng and GUAN Ke-ying |
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| Affiliation: | Department of Basic Science, University of Petroleum, Beijing 102200, China;Department of Mathematics, Northern Jiaotong University, Beijing 100044, China |
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| Abstract: | A way of transforming first order nonlinear PDE to first order quasilinear PDE or integrable first order PDE by using Lie group method is presented. The presented way can be applied to some first order nonlinear PDE's which admit one or two Lie groups and have two independent variables,especially to Hamilton-Jacobi equations of some Lagrange systems which have one degree of freedom. |
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| Keywords: | Lie group first order PDE Hamilton-Jacobi equation integrability. |
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