Abstract In this paper, a Birkhoff--Noether method of solving ordinary differential equations is presented. The differential equations can be expressed in terms of Birkhoff's equations. The first integrals for differential equations can be found by using the Noether theory for Birkhoffian systems. Two examples are given to illustrate the application of the method.
Received: 28 April 2006
Revised: 25 August 2006
Accepted manuscript online:
PACS:
02.30.Hq
(Ordinary differential equations)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10472040) and Doctoral Programme Foundation of Institution of Higher Education of China (Grant No 20040007022).
Cite this article:
Shang Mei(尚玫), Guo Yong-Xin(郭永新), and Mei Feng-Xiang (梅凤翔) A Birkhoff-Noether method of solving differential equations 2007 Chinese Physics 16 292
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