Journal of Lie Theory Vol. 13, No. 1, pp. 167188 (2003) 

C$^{\infty}$Symmetries and Reduction of Equations Without Lie Point SymmetriesC. Muriel and J. L. RomeroC. MurielDpto. Matemáticas Facultad de Ciencias Universidad de Cádiz Apto. 40, 11510 Puerto Real Cádiz, Spain concepcion.muriel@uca.es 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.
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