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Invariants and invariant description of second-order ODEs with three infinitesimal symmetries. I
Responsible organisation
2007 (English)In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 12, no 8, p. 1370-1378Article in journal (Refereed) Published
Abstract [en]

Lie's group classification of ODEs shows that the second-order equations can possess one, two, three or eight infinitesimal symmetries. The equations with eight symmetries and only these equations can be linearized by a change of variables. Lie showed that the latter equations are at most cubic in the first derivative and gave a convenient invariant description of all linearizable equations. Our aim is to provide a similar description of the equations with three symmetries. There are four different types of such equations. We present here the candidates for all four types. We give an invariant test for existence of three symmetries for one of these candidates.

Place, publisher, year, edition, pages
Amsterdam: Elsevier , 2007. Vol. 12, no 8, p. 1370-1378
Keywords [en]
Invariants, Lie group analysis
National Category
Mathematics
Identifiers
URN: urn:nbn:se:bth-8994Local ID: oai:bth.se:forskinfo9FF2C8283E43F651C125733E00475054OAI: oai:DiVA.org:bth-8994DiVA, id: diva2:836770
Available from: 2012-09-18 Created: 2007-08-21 Last updated: 2017-12-04Bibliographically approved

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CiteExportLink to record
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  • apa
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