Erzeugung nichtlinearer gewöhnlicher Differentialgleichungen mit vorgegebener Lie-Algebra von Punktsymmetrien

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.