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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Shnider, S., Winternitz, P. Nonlinear equations with superposition principles and the theory of transitive primitive Lie algebras. Lett Math Phys 8, 69–78 (1984). https://doi.org/10.1007/BF00420043
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DOI: https://doi.org/10.1007/BF00420043