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Remarks on the symmetry Lie algebras of first integrals of scalar third-order ordinary differential equations with maximal symmetry. (English) Zbl 0919.34009

Summary: The authors present first integrals of third-order ordinary differential equations with maximal symmetry by considering Lie symmetries of the equations. Properties of these integrals and algebras of their symmetries are discussed and a connection to higher-order equations and maximal symmetry is pursued. Second-order and third-order equations with maximal symmetry are shown to be anomalies in the group theoretic approach to understanding \(n\)th-order equations with maximal symmetry and their first integrals.

MSC:

34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
17B66 Lie algebras of vector fields and related (super) algebras
37C80 Symmetries, equivariant dynamical systems (MSC2010)
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