Ordinary differential equations described by their Lie symmetry algebra

Abstract

The theory of Lie remarkable equations, 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.

17 pages

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Cited by in corpus (6)

• Lie remarkable partial differential equations characterized by Lie algebras of point symmetries
• Consistent approximate Q-conditional symmetries of PDEs: application to a hyperbolic reaction-diffusion-convection equation
• Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation
• The global symmetry group of first order differential equations and the global rectification theorem
• Hidden symmetries, hidden conservation laws and exact solutions of dispersionless Nyzhnyk equation
• A study on Darboux polynomials and their significance in determining other integrability quantifiers: A case study in third-order nonlinear ordinary differential equations