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Symmetry 2010, 2(2), 658-706; doi:10.3390/sym2020658

Lie Symmetries of Differential Equations: Classical Results and Recent Contributions

Department of Mathematics, University of Messina, Contrada Papardo, Viale Ferdinando Stagno d’Alcontres 31, I–98166 Messina, Italy
Received: 2 January 2010 / Accepted: 30 March 2010 / Published: 8 April 2010
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
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Abstract

Lie symmetry analysis of differential equations provides a powerful and fundamental framework to the exploitation of systematic procedures leading to the integration by quadrature (or at least to lowering the order) of ordinary differential equations, to the determination of invariant solutions of initial and boundary value problems, to the derivation of conservation laws, to the construction of links between different differential equations that turn out to be equivalent. This paper reviews some well known results of Lie group analysis, as well as some recent contributions concerned with the transformation of differential equations to equivalent forms useful to investigate applied problems.
Keywords: lie point symmetries; invariance of differential equations; invertible mappings between differential equations lie point symmetries; invariance of differential equations; invertible mappings between differential equations
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Oliveri, F. Lie Symmetries of Differential Equations: Classical Results and Recent Contributions. Symmetry 2010, 2, 658-706.

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