 Lie symmetries for Lie systems: Applications to systems of ODEs and PDEsP.G. Estévez, F.J. Herranz, J. de Lucas and C. Sardón Applied Mathematics and Computation, 2016, vol. 273, issue C, 435-452 Abstract: A Lie system is a nonautonomous system of first-order differential equations admitting a superposition rule, i.e., a map expressing its general solution in terms of a generic family of particular solutions and some constants. Using that a Lie system can be considered as a curve in a finite-dimensional Lie algebra of vector fields, a so-called Vessiot–Guldberg Lie algebra, we associate every Lie system with a Lie algebra of Lie point symmetries induced by the Vessiot–Guldberg Lie algebra. This enables us to derive Lie symmetries of relevant physical systems described by first- and higher-order systems of differential equations by means of Lie systems in an easier way than by standard methods. A generalization of our results to partial differential equations is introduced. Among other applications, Lie symmetries for several new and known generalizations of the real Riccati equation are studied. Keywords: Lie symmetry; Lie system; Superposition rule; Lie algebra; Ordinary differential equation; Partial differential equation; Riccati equation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:273:y:2016:i:c:p:435-452 DOI: 10.1016/j.amc.2015.09.078 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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