We give a geometrical characterization of λ-prolongations of vector fields, and hence of λ-symmetries of ODEs. This allows an extension to the case of PDEs and systems of PDEs; in this context the central object is a horizontal 1-form μ, and we speak of μ-prolongations of vector fields and μ-symmetries of PDEs. We show that these are as good as standard symmetries in providing symmetry reduction of PDEs and systems, and explicit invariant solutions.
On the geometry of lambda-symmetries and PDE reduction / G. Gaeta, P. Morando. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - 37:27(2004 Jul 09), pp. 6955-6975. [10.1088/0305-4470/37/27/007]
On the geometry of lambda-symmetries and PDE reduction
G. GaetaPrimo
;P. MorandoUltimo
2004
Abstract
We give a geometrical characterization of λ-prolongations of vector fields, and hence of λ-symmetries of ODEs. This allows an extension to the case of PDEs and systems of PDEs; in this context the central object is a horizontal 1-form μ, and we speak of μ-prolongations of vector fields and μ-symmetries of PDEs. We show that these are as good as standard symmetries in providing symmetry reduction of PDEs and systems, and explicit invariant solutions.
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