Computation of local symmetries of second-order ordinary differential equations by the Cartan equivalence method |
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Authors: | Yu. R. Romanovskii |
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Affiliation: | (1) Institute of Software Systems, Russian Academy of Sciences, Pereslavl-Zalesskii |
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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. Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 75–91, July, 1996. |
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Keywords: | group analysis of differential equations local symmetries Cartan equivalence method |
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