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Abstract: We analyze families of non-autonomous systems of first-order ordinarydifferential equations admitting a common time-dependent superposition rule,i.e., a time-dependent map expressing any solution of each of these systems interms of a generic set of particular solutions of the system and someconstants. We next study relations of these families, called Lie families, withthe theory of Lie and quasi-Lie systems and apply our theory to provide commontime-dependent superposition rules for certain Lie families.



Autor: Jose F. Carinena, Janusz Grabowski, Javier de Lucas

Fuente: https://arxiv.org/







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