Superposition rules, Lie theorem and partial differential equations

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dc.creatorCariñena, José F.
dc.creatorGrabowski, Janusz
dc.creatorMarmo, Giuseppe
dc.date2006-10-06
dc.date.accessioned2026-07-07T11:28:12Z
dc.date.available2026-07-07T11:28:12Z
dc.descriptionA rigorous geometric proof of the Lie's Theorem on nonlinear superposition rules for solutions of non-autonomous ordinary differential equations is given filling in all the gaps present in the existing literature. The proof is based on an alternative but equivalent definition of a superposition rule: it is considered as a foliation with some suitable properties. The problem of uniqueness of the superposition function is solved, the key point being the codimension of the foliation constructed from the given Lie algebra of vector fields. Finally, as a more convincing argument supporting the use of this alternative definition of superposition rule, it is shown that this definition allows an immediate generalization of Lie's Theorem for the case of systems of partial differential equations.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0610013
dc.identifierhttp://arxiv.org/abs/math-ph/0610013
dc.identifierRept.Math.Phys.60:237-258,2007
dc.identifierdoi:10.1016/S0034-4877(07)80137-6
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/196366
dc.subjectMathematical Physics
dc.subject34A26; 22E70
dc.titleSuperposition rules, Lie theorem and partial differential equations
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