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On the geometry of lambda-symmetries, and PDEs reduction

G. Gaeta·P. Morando
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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 one-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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G. Gaeta, P. Morando. 2004-06-23. On the geometry of lambda-symmetries, and PDEs reduction. https://doi.org/10.1088/0305-4470/37/27/007

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