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Erzeugung nichtlinearer gewöhnlicher Differentialgleichungen mit vorgegebener Lie-Algebra von Punktsymmetrien

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Campoamor Stursberg, Otto Ruttwig (2004) Erzeugung nichtlinearer gewöhnlicher Differentialgleichungen mit vorgegebener Lie-Algebra von Punktsymmetrien. Journal of Lie Theory, 14 (2). pp. 537-541. ISSN 0949-5932

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Official URL: http://www.emis.ams.org/journals/JLT/vol.14_no.2/campoala2e.pdf


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Abstract

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.


Item Type:Article
Additional Information:

Generation of nonlinear ordinary differential equations with given Lie algebra of point symmetries

Uncontrolled Keywords:Symmetry; nth-order ordinary differential equation; symmetry algebra; SL(2,R)
Subjects:Sciences > Mathematics > Algebra
ID Code:21902
Deposited On:18 Jun 2013 07:00
Last Modified:12 Dec 2018 15:13

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