中国物理B ›› 2007, Vol. 16 ›› Issue (2): 292-295.doi: 10.1088/1009-1963/16/2/004

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A Birkhoff-Noether method of solving differential equations

郭永新1, 尚玫2, 梅凤翔2   

  1. (1)Department of Physics, Liaoning University, Shenyang 110036, China; (2)Faculty of Science, Beijing Institute of Technology, Beijing 100081, China
  • 收稿日期:2006-04-28 修回日期:2006-08-25 出版日期:2007-02-20 发布日期:2007-02-20
  • 基金资助:
    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).

A Birkhoff-Noether method of solving differential equations

Shang Mei(尚玫)a)†, Guo Yong-Xin(郭永新)b), and Mei Feng-Xiang (梅凤翔)a)   

  1. a Faculty of Science, Beijing Institute of Technology, Beijing 100081, China; b Department of Physics, Liaoning University, Shenyang 110036, China
  • Received:2006-04-28 Revised:2006-08-25 Online:2007-02-20 Published:2007-02-20
  • Supported by:
    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).

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摘要： 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.

关键词: differential equation, Birkhoffian system, Noether theory, first integral

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.

Key words: differential equation, Birkhoffian system, Noether theory, first integral

中图分类号:  (Ordinary differential equations)

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