This article is cited in 11 papers

Computation of local symmetries of second-order ordinary differential equations by the Cartan equivalence method

Yu. R. Romanovskii

Program Systems Institute of RAS

Abstract: The Cartan equivalence method is used to find out if a given equation has a nontrivial Lie group of point symmetries. In particular, we compute invariants that permit one to recognize equations with a three-dimensional symmetry group. An effective method to transform the Lie system (the system of partial differential equations to be satisfied by the infinitesimal point symmetries) into a formally integrable form is given. For equations with a three-dimensional symmetry group, the formally integrable form of the Lie system is found explicitly.

UDC: 517

Received: 09.04.1992
Revised: 05.03.1996

DOI: 10.4213/mzm1805

 English version: Mathematical Notes, 1996, 60:1, 56–67

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