Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations
A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equatio...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/23854 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/23854 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.9 512 Lie systems Vessiot-Guldberg-Lie algebra Superposition rule SODE Lie systems Álgebra Ecuaciones diferenciales 1201 Álgebra 1202.07 Ecuaciones en Diferencias |
| Sumario: | A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebra. In particular, well-known types, such as the Milne-Pinney or Kummer-Schwarz equations, are recovered as special cases of this classification. The analogous problem for systems of second-order differential equations in the real plane is considered for a special case that enlarges the generalized Ermakov systems. |
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