Nonlocal aspects of λ-symmetries and ODEs reduction
نویسنده
چکیده
A reduction method of ODEs not possessing Lie point symmetries makes use of the so called λ-symmetries (C. Muriel and J. L. Romero, IMA J. Appl. Math. 66, 111-125, 2001). The notion of covering for an ODE Y is used here to recover λ-symmetries of Y as nonlocal symmetries. In this framework, by embedding Y into a suitable system Y ′ determined by the function λ, any λ-symmetry of Y can be recovered by a local symmetry of Y . As a consequence, the reduction method of Muriel and Romero follows from the standard method of reduction by differential invariants applied to Y . PACS numbers: 02.30.Hq AMS classification scheme numbers: 34C14
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