Characterisation of the algebraic properties of first integrals of scalar ordinary differential equations of maximal symmetry

DOI10.1006/jmaa.1997.5506zbMath0879.34052OpenAlexW2123291279MaRDI QIDQ1365090

G. P. Flessas, Keshlan S. Govinder, Peter G. L. Leach

Publication date: 19 January 1998

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1997.5506

zbMATH Keywords

first integralsmaximal symmetryequivalence of contact symmetrieslinear \(n\)th order scalar ordinary differential equationsnon-Cartan symmetries

Mathematics Subject Classification ID

Related Items (11)

Some variational principles associated with ODEs of maximal symmetry. I: Equations in canonical form ⋮ Algebraic properties of first integrals for scalar linear third-order ODEs of maximal symmetry ⋮ First integrals and reduction of a class of nonlinear higher order ordinary differential equations. ⋮ Characterization of symmetry properties of first integrals for submaximal linearizable third-order ODEs ⋮ First integrals and Hamiltonians of some classes of ODEs of maximal symmetry ⋮ First Integrals and Parametric Solutions for Equations Integrable Through Lie Symmetries ⋮ Symmetries, integrals and solutions of ordinary differential equations of maximal symmetry ⋮ Complete symmetry groups of ordinary differential equations and their integrals: Some basic considerations ⋮ Nonlinear ordinary differential equations: A discussion on symmetries and singularities ⋮ Algebraic properties of first integrals for systems of second-order ordinary differential equations of maximal symmetry ⋮ Exceptional properties of second and third order ordinary differential equations of maximal symmetry

Uses Software

• LIE

Cites Work

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• The algebraic structure of the first integrals of third-order linear equations
• Symmetry Lie algebras of \(n\)th order ordinary differential equations
• THE LINEAR SYMTRIES OF A NONLINEAR DIFFERENTIAL EQUATION
• Maximal subalgebra associated with a first integral of a system possessing sl(3,R) algebra
• Classification of Second-Order Ordinary Differential Equations Admitting Lie Groups of Fibre-Preserving Point Symmetries
• Subalgebras of real three- and four-dimensional Lie algebras
• Analysis and solution of a nonlinear second-order differential equation through rescaling and through a dynamical point of view
• Hidden and contact symmetries of ordinary differential equations
• LIE, a PC program for Lie analysis of differential equations

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