中国物理B ›› 2008, Vol. 17 ›› Issue (8): 2764-2765.doi: 10.1088/1674-1056/17/8/003

• GENERAL • 上一篇    下一篇

Conformal invariance and integration of first-order differential equations

何 光1, 梅凤翔2   

  1. (1)School of Aerospace Science and Engineering, Beijing Institute of Technology, Beijing 100081, China; (2)School of Science, Beijing Institute of Technology, Beijing 100081, China
  • 收稿日期:2007-11-11 修回日期:2007-11-23 出版日期:2008-08-20 发布日期:2008-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025) and the Doctoral Programme Foundation of Institution of Higher Education of China (Grant No 20040007022).

Conformal invariance and integration of first-order differential equations

He Guang(何光)a)† and Mei Feng-Xiang(梅凤翔)b)   

  1. a School of Aerospace Science and Engineering, Beijing Institute of Technology, Beijing 100081, China; b School of Science, Beijing Institute of Technology, Beijing 100081, China
  • Received:2007-11-11 Revised:2007-11-23 Online:2008-08-20 Published:2008-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025) and the Doctoral Programme Foundation of Institution of Higher Education of China (Grant No 20040007022).

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摘要： This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system.

Abstract: This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system.

Key words: differential equation, conformal invariance, Noether theory, integration

中图分类号:  (Partial differential equations)

  • 02.30.Jr
45.05.+x (General theory of classical mechanics of discrete systems)