Nonlinear Phenomena in Complex Systems, 2008, Vol.11, No.2, pp.205-211

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2008, Vol.11, No.2, pp.205-211

Second-order, Third-order, and nth-order Ordinary Differential Equations: How the Exceptional Became Unexceptional.
P. G. L. Leach

Second- and third-order scalar ordinary differential equations of maximal symmetry in the traditional sense of point, respectively contact, symmetry are examined for the mappings they produce in fundamental first integrals. The properties of the ``exceptional symmetries'', ie those not considered to be generic to scalar equations of maximal symmetry, can be recast into a form which is applicable to all such equations of maximal symmetry. Thereby the exceptional symmetries are rendered unexceptional.
Key words: Lie symmetries; noncartan symmetries; generalised symmetries

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