Lie symmetry and conserved quantity of a system of first-order differential equations
Xu Xue-Jun (许学军)ab, Mei Feng-Xiang (梅凤翔)a, Zhang Yong-Fa (张永发)a
a Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China; b Department of Physics, Zhejiang Normal University, Jinhua 321004, China
Abstract This paper focuses on studying the Lie symmetry and a conserved quantity of a system of first-order differential equations. The determining equations of the Lie symmetry for a system of first-order differential equations, from which a kind of conserved quantity is deduced, are presented. And their general conclusion is applied to a Hamilton system, a Birkhoff system and a generalized Hamilton system. Two examples are given to illustrate the application of the results.
Received: 22 April 2005
Accepted manuscript online:
PACS:
02.30.Hq
(Ordinary differential equations)
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10272021) and the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022).
Cite this article:
Xu Xue-Jun (许学军), Mei Feng-Xiang (梅凤翔), Zhang Yong-Fa (张永发) Lie symmetry and conserved quantity of a system of first-order differential equations 2006 Chinese Physics 15 19
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