Nonlocal interpretation of $λ$-variational symmetry-reduction method

Ferraioli, D. Catalano; Morando, P.

Nonlocal interpretation of $λ$-variational symmetry-reduction method

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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 2006 \emph{Variational $C^{\infty}$-symmetries and Euler-Lagrange equations} J. Differential equations \textbf{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.