Nonlinear equations with superposition principles and the theory of transitive primitive Lie algebras |
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| Authors: | S. Shnider P. Winternitz |
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| Affiliation: | (1) Department of Mathematics, McGill University, H3A 2KB Montreal, Quebec, Canada;(2) Present address: Department of Mathematics, Ben Gurion University, P.O. Box 653, 84105 Beersheva, Israel;(3) Centre de recherche de mathématiques appliquèes, Université de Montréal, CP 6128 Montreal, Quebec, Canada, H3C 3J7 |
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| Abstract: | The classification of systems of nonlinear ordinary differential equations with superposition principles is reduced to a classification of transitive primitive Lie algebras. Each system can be associated with the transitive primitive action of a Lie group G on a homogenous space G/H, where H is a maximal subgroup of G. The equations can have specific polynomial or rational nonlinearities. |
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