An Elementary Demonstration of the Existence of $s\ell(3,R)$ Symmetry for all Second-Order Linear Ordinary Differential Equations

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Previous article Next article An Elementary Demonstration of the Existence of $s\ell(3,R)$ Symmetry for all Second-Order Linear Ordinary Differential EquationsK. S. Govinder and P. G. L. LeachK. S. Govinder and P. G. L. Leachhttps://doi.org/10.1137/S0036144597316838PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractAll second-order linear ordinary differential equations are shown in an elementary way to possess the symmetry algebra ${s}\ell(2,R)$.[1] M. Aguirre and , J. Krause, SL(3,R) as the group of symmetry transformations for all one‐dimensional linear systems, J. Math. Phys., 29 (1988), 9–15 10.1063/1.528139 89g:58184 CrossrefISIGoogle Scholar[2] Robert Anderson and , Suzanne Davison, A generalization of Lie’s “counting” theorem for second‐order ordinary differential equations, J. Math. Anal. Appl., 48 (1974), 301–315 51:971 CrossrefISIGoogle Scholar[3] Nedialko Nedialkov and , Kenneth Jackson, An interval Hermite‐Obreschkoff method for computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation, Kluwer Acad. Publ., Dordrecht, 1999, 289–310 1744280 Google Scholar[4] L. M. Berković, Glyden–Mes˘c˘erskii problem, Celest. Mech., 24 (1981), pp. 407–429. csm CLMCAV 0008-8714 Celest. Mech. CrossrefISIGoogle Scholar[5] Google Scholar[6] F. Mahomed and , P. Leach, The Lie algebra sl(3,R) and linearization, Quaestiones Math., 12 (1989), 121–139 91d:58221 CrossrefGoogle Scholar[7] F. Mahomed and , P. Leach, Symmetry Lie algebras of nth order ordinary differential equations, J. Math. Anal. Appl., 151 (1990), 80–107 91h:58091 CrossrefISIGoogle Scholar[8] C. Wulfman and , B. Wybourne, The Lie group of Newton’s and Lagrange’s equations for the harmonic oscillator, J. Phys. A, 9 (1976), 507–518 10.1088/0305-4470/9/4/007 54:479 CrossrefGoogle ScholarKeywordslinear differential equations$s\ell(3R)$ Previous article Next article FiguresRelatedReferencesCited byDetails Analysis of modified Painlevé–Ince equations28 May 2020 | Ricerche di Matematica, Vol. 71, No. 1 Cross Ref Maximally superintegrable systems in flat three-dimensional space are linearizableJournal of Mathematical Physics, Vol. 62, No. 1 Cross Ref Symmetry analysis of the Klein–Gordon equation in Bianchi I spacetimesInternational Journal of Geometric Methods in Modern Physics, Vol. 12, No. 03 Cross Ref Symmetry group classification of ordinary differential equations: Survey of some results1 January 2007 | Mathematical Methods in the Applied Sciences, Vol. 30, No. 16 Cross Ref Lie symmetry algebra of one-dimensional nonconservative dynamical systems11 September 2007 | Chinese Physics, Vol. 16, No. 9 Cross Ref Integrability analysis of the Emden-Fowler equation21 January 2013 | Journal of Nonlinear Mathematical Physics, Vol. 14, No. 3 Cross Ref Symmetries of First Integrals and Their Associated Differential EquationsJournal of Mathematical Analysis and Applications, Vol. 235, No. 1 Cross Ref Volume 40, Issue 4| 1998SIAM Review History Published online:02 August 2006 InformationCopyright © 1998 Society for Industrial and Applied MathematicsKeywordslinear differential equations$s\ell(3R)$MSC codes34A30PDF Download Article & Publication DataArticle DOI:10.1137/S0036144597316838Article page range:pp. 945-946ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics