EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 13, No. 1, pp. 167--188 (2003)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



C$^{\infty}-$Symmetries and Reduction of Equations Without Lie Point Symmetries

C. Muriel and J. L. Romero

C. Muriel
Dpto. Matemáticas
Facultad de Ciencias
Universidad de Cádiz
Apto. 40, 11510 Puerto Real
Cádiz, Spain

Abstract: It is proved that several usual methods of reduction for ordinary di\-ffe\-ren\-tial equations, that do not come from the Lie theory, are derived from the exis\-ten\-ce of $C^\infty$-sy\-mme\-tries. This kind of sy\-mme\-tries is also applied to obtain two successive reductions of an equation that lacks Lie point sy\-mme\-tries but is a reduced equation of another one with a three dimensional Lie algebra of point symmetries. Some relations between $C^\infty$-sy\-mme\-tries and potential sy\-mme\-tries are also studied.

Full text of the article:

Electronic fulltext finalized on: 22 Nov 2002. This page was last modified: 3 Jan 2003.

© 2002 Heldermann Verlag
© 2002--2003 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition