A standard method based on the use of differential invariants of a Lie group, G, enables us to reduce any ordinary differential equation invariant under the action of G. We showthat this method is applicable to vector fields more general than those associated with Lie symmetries. We characterize all such vector fields and study their relationship with nonlocal symmetries and λ- symmetries (Govinder K S and Leach P G L 1995 J. Phys. A: Math. Gen. 28 5349–59, Muriel C and Romero L 2001 IMA J. Appl. Math. 66 111–25).
On the reduction methods for ordinary differential equations
PUCCI, Edvige;SACCOMANDI, Giuseppe
2002
Abstract
A standard method based on the use of differential invariants of a Lie group, G, enables us to reduce any ordinary differential equation invariant under the action of G. We showthat this method is applicable to vector fields more general than those associated with Lie symmetries. We characterize all such vector fields and study their relationship with nonlocal symmetries and λ- symmetries (Govinder K S and Leach P G L 1995 J. Phys. A: Math. Gen. 28 5349–59, Muriel C and Romero L 2001 IMA J. Appl. Math. 66 111–25).File in questo prodotto:
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