Nonlocal interpretation of λ-variational symmetry-reduction method

In this paper we give a geometric interpretation of a reduction method based on the so called λ-variational symmetry (C. Muriel, J.L. Romero and P. Olver 2006Variational C∞-symmetries and Euler-Lagrange equations J. Differential equations 222 164-184). In general this allows only a partial reduction but it is particularly suitable for the reduction of variational ODEs with a lack of computable local symmetries. We show that this method is better understood as a nonlocal symmetry-reduction. PACS numbers: 02.30.Hq AMS classification scheme numbers: 37K05, 34C14, 70S10