Original Articles

THE LIE ALGEBRA sl(3, R) AND LINEARIZATION

Published in: Quaestiones Mathematicae
Volume 12 , issue 2 , 1989 , pages: 121–139

DOI: 10.1080/16073606.1989.9632170

Author(s): FM MAHOMED Centre for Nonlinear Studies and Department of Computational and Applied Mathematics, South Africa , P , G L LEACH Centre for Nonlinear Studies and Department of Computational and Applied Mathematics, South Africa

Keywords: 34A34 , 22E70

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Abstract

In a previous paper (see [10]) we established the form of second-order ordinary differential equations with two commuting symmetries (in canonical form G₁ = ∂/∂, G₂ = ∂/∂_q, G₂ ≠ p(q,t)G₁) which have the Lie algebra sl(3, R). In this paper we determine the conditions under which an equation with two non-commuting (non-proportional) symmetries possesses the Lie algebra sl(3, R). We also obtain the most general nonlinear equation at most linear in the first derivative which has sl(3, R) algebra.

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