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Invariants and invariant description of second-order ODEs with three infinitesimal symmetries. II.
Responsible organisation
2008 (English)In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, Vol. 13, no 6, 1015-1020 p.Article in journal (Refereed) Published
Abstract [en]

The second-order ordinary differential equations can have one, two, three or eight independent symmetries. Sophus Lie showed that the equations with eight symmetries and only these equations can be linearized by a change of variables. Moreover he demonstrated that these equations are at most cubic in the first derivative and gave a convenient invariant description of all linearizable equations. We provide a similar description of the equations with three symmetries. There are four different types of such equations. Classes of equations belonging to one of these types were studied in N.H. Ibragimov and S.V. Meleshko, Invariants and invariant description of second-order ODEs with three infinitesimal symmetries. I, Communications in Nonlinear Science and Numerical Simulation, Vol. 12, No. 8, 2007, pp. 1370--1378. Namely, we presented there the candidates for all four types and studied one of these candidates.The present paper is devoted to other three candidates.

Place, publisher, year, edition, pages
The Netherlands: ELSEVIER SCIENCE BV , 2008. Vol. 13, no 6, 1015-1020 p.
Keyword [en]
Invariants, second-order ODEs, infinitesimal symmetries
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:bth-8838DOI: 10.1016/j.cnsns.2006.03.011ISI: 000254602300001Local ID: oai:bth.se:forskinfo2640DD4C9DFE3D67C12573BE00713C35OAI: oai:DiVA.org:bth-8838DiVA: diva2:836593
Available from: 2012-09-18 Created: 2007-12-27 Last updated: 2015-06-30Bibliographically approved

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