Invariants and invariant description of second-order ODEs with three infinitesimal symmetries. I
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences2007 (English)In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, Vol. 12, no 8, 1370-1378 p.Article in journal (Refereed) Published
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, 1370-1378 p.
Invariants, Lie group analysis
IdentifiersURN: urn:nbn:se:bth-8994Local ID: oai:bth.se:forskinfo9FF2C8283E43F651C125733E00475054OAI: oai:DiVA.org:bth-8994DiVA: diva2:836770