Kamran, Niky; Olver, Peter J. Equivalence of differential operators. (English) Zbl 0715.47032 SIAM J. Math. Anal. 20, No. 5, 1172-1185 (1989). The authors treat the following equivalence problem: when two second order operators on the real line can be transformed into each other by an appropriate change of variables. The equivalence has two different interpretations, depending on whether one wishes to preserve the differential expression or the Lie brackets between the operators. Both versions are considered and solved using the Cartan method. Reviewer: G.Caristi Cited in 13 Documents MSC: 47E05 General theory of ordinary differential operators 58A15 Exterior differential systems (Cartan theory) 34A26 Geometric methods in ordinary differential equations Keywords:Cartan equivalence method; second order operators; change of variables; Lie brackets PDFBibTeX XMLCite \textit{N. Kamran} and \textit{P. J. Olver}, SIAM J. Math. Anal. 20, No. 5, 1172--1185 (1989; Zbl 0715.47032) Full Text: DOI