The theory of Lie remarkable equations, \emph{i.e.}, differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector fields on $\mathbb{R}^k$ and characterize Lie remarkable equations admitted by the considered Lie algebras.
Ordinary differential equations described by their Lie symmetry algebra
VITOLO, Raffaele
2014-01-01
Abstract
The theory of Lie remarkable equations, \emph{i.e.}, differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector fields on $\mathbb{R}^k$ and characterize Lie remarkable equations admitted by the considered Lie algebras.File in questo prodotto:
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