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• W2080768110 abstract "We use Elie Cartan's method of equivalence to give a complete classification, in terms of differential invariants, of second-order ordinary differential equations admitting Lie groups of fibre-preserving point symmetries. We then apply our results to the determination of all second-order equations which are equivalent, under fibre-preserving transformations, to the free particle equation. In addition we present those equations of Painlevé type which admit a transitive symmetry group. Finally we determine the symmetry group of some equations of physical interest, such as the Duffing and Holmes-Rand equations, which arise as models of non-linear oscillators." @default.
• W2080768110 created "2016-06-24" @default.
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• W2080768110 date "1989-03-01" @default.
• W2080768110 modified "2023-10-14" @default.
• W2080768110 title "Classification of Second-Order Ordinary Differential Equations Admitting Lie Groups of Fibre-Preserving Point Symmetries" @default.
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• W2080768110 doi "https://doi.org/10.1112/plms/s3-58.2.387" @default.
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