Open Access
2012 Hidden and Not So Hidden Symmetries
P. G. L. Leach, K. S. Govinder, K. Andriopoulos
J. Appl. Math. 2012: 1-11 (2012). DOI: 10.1155/2012/890171


Hidden symmetries entered the literature in the late Eighties when it was observed that there could be gain of Lie point symmetry in the reduction of order of an ordinary differential equation. Subsequently the reverse process was also observed. Such symmetries were termed “hidden”. In each case the source of the “new” symmetry was a contact symmetry or a nonlocal symmetry, that is, a symmetry with one or more of the coefficient functions containing an integral. Recent work by Abraham-Shrauner and Govinder (2006) on the reduction of partial differential equations demonstrates that it is possible for these “hidden” symmetries to have a point origin. In this paper we show that the same phenomenon can be observed in the reduction of ordinary differential equations and in a sense loosen the interpretation of hidden symmetries.


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P. G. L. Leach. K. S. Govinder. K. Andriopoulos. "Hidden and Not So Hidden Symmetries." J. Appl. Math. 2012 1 - 11, 2012.


Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1239.34031
MathSciNet: MR2880831
Digital Object Identifier: 10.1155/2012/890171

Rights: Copyright © 2012 Hindawi

Vol.2012 • 2012
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