Publicado

2005-07-01

Symmetries and integration of differential equations

Palabras clave:

Ordinary differential equations, Symmetries, 2000 Mathematics Subject Classification, Primary: 34A26, 54H15, Secondary: 58D19, 35F05 (en)

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Autores/as

  • Gerardo Torres del Castillo Universidad Autónoma de Puebla, México
  • Magdalena Marciano Melchor Universidad Autónoma de Puebla, México

Abstract. A proof of the Lie theorem which relates the symmetries of a first order differential equation (or of a linear differential form) with its integrating factors is given. It is shown that a similar result partially applies for systems of linear differential forms and ordinary differential equations of any order.

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Citas

G. F. Simmons, Differential Equations. With Applications and Historical Notes, 2nd ed., 9. McGraw-Hill, New York, 1991.

N. H. Ibragimov, Sophus Lie and Harmony in Mathematical Physics, on the 150th Anniversary of His Birth, The Mathematical Intelligencer 16, 20 (1994).

H. Stephani, Differential Equations: Their Solution Using Symmetries, Cambridge University Press, Cambridge, 1989.

L. Dresner, Applications of Lie’s Theory of Ordinary and Partial Differential Equations, Institute of Physics, Bristol, 1999.

P. E. Hydon, Symmetry Methods for Differential Equations: A Beginner’s Guide, Cambridge University Press, Cambridge, 2000.

C. Von Westenholz, Differential Forms in Mathematical Physics, North-Holland, Amsterdam, 1981.

Licencia

Creative Commons License

Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.