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arXiv · 0708.3144

Noether theorem for mu-symmetries

G. Cicogna·G. Gaeta
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Abstract

We give a version of Noether theorem adapted to the framework of mu-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of lambda-symmetries, and connects mu-symmetries of a Lagrangian to a suitably modified conservation law. In some cases this "mu-conservation law'' actually reduces to a standard one; we also note a relation between mu-symmetries and conditional invariants. We also consider the case where the variational principle is itself formulated as requiring vanishing variation under mu-prolonged variation fields, leading to modified Euler-Lagrange equations. In this setting mu-symmetries of the Lagrangian correspond to standard conservation laws as in the standard Noether theorem. We finally propose some applications and examples.

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G. Cicogna, G. Gaeta. 2007-08-23. Noether theorem for mu-symmetries. https://doi.org/10.1088/1751-8113/40/39/013

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