On the geometry of lambda-symmetries, and PDEs reduction

Details On the geometry of lambda-symmetries, and PDEs reduction On the geometry of lambda-symmetries, and PDEs reduction

2004-06-23

arxiv.org/abs/math-ph/0406051v1

J. Phys. A 37 (2004), 6955-6975

Physics

Mathematical Physics

Scientific paper

10.1088/0305-4470/37/27/007

We give a geometrical characterization of $\lambda$-prolongations of vector fields, and hence of $\lambda$-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 $\mu$, and we speak of $\mu$-prolongations of vector fields and $\mu$-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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