On the relation between standard and $μ$-symmetries for PDEs

Details On the relation between standard and $μ$-symmetries for PDEs On the relation between standard and $μ$-symmetries for PDEs

2004-09-02

arxiv.org/abs/math-ph/0409004v1

J. Phys. A: Math. Gen., Vol. 37, 9467-9486 (2004)

Physics

Mathematical Physics

25 pages, no figures, latex. to be published in J. Phys. A

Scientific paper

10.1088/0305-4470/37/40/010

We give a geometrical interpretation of the notion of $\mu$-prolongations of vector fields and of the related concept of $\mu$-symmetry for partial differential equations (extending to PDEs the notion of $\lambda$-symmetry for ODEs). We give in particular a result concerning the relationship between $\mu$-symmetries and standard exact symmetries. The notion is also extended to the case of conditional and partial symmetries, and we analyze the relation between local $\mu$-symmetries and nonlocal standard symmetries.

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