Erzeugung nichtlinearer gewöhnlicher Differentialgleichungen mit vorgegebener Lie-Algebra von Punktsymmetrien

The goal of this paper is to show that for every n � 4 there exists an ordinary nth-order differential equation which admits exactly SL(2,R) in the usual representation X1 = x · @x, X2 = @x, X3 = x2 · @x, as the corresponding symmetry algebra. At first, the author presents such an ordinary different...

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Detalles Bibliográficos
Autor: Campoamor Stursberg, Otto-Rudwig
Tipo de recurso: artículo
Fecha de publicación:2004
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/50711
Acceso en línea:https://hdl.handle.net/20.500.14352/50711
Access Level:acceso abierto
Palabra clave:512
Symmetry
Nth-order ordinary differential equation
Symmetry algebra
SL(2R)
Álgebra
1201 Álgebra
Descripción
Sumario:The goal of this paper is to show that for every n � 4 there exists an ordinary nth-order differential equation which admits exactly SL(2,R) in the usual representation X1 = x · @x, X2 = @x, X3 = x2 · @x, as the corresponding symmetry algebra. At first, the author presents such an ordinary differential equation (ODE) for which the above generators are symmetries, then this ODE is modified by an additional term to exclude further symmetries. The proofs are presented rather as argumentations, whereas the concrete calculations are left to the reader.