Noether theorem for mu-symmetries

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.

28 pages, to appear in J. Phys. A

References in corpus (5)

• On the geometry of lambda-symmetries, and PDEs reduction
• On the relation between standard and $\mu$-symmetries for PDEs
• Conservation laws of scaling-invariant field equations
• Nonlocal aspects of $\lambda$-symmetries and ODEs reduction
• Configurational invariants of Hamiltonian systems

Cited by in corpus (6)

• Reduction of systems of first-order differential equations via Lambda-symmetries
• A generalization of λ-symmetry reduction for systems of ODEs: σ-symmetries
• ${\mathcal{C}}^{\infty }$-symmetries of distributions and integrability
• A gauge-theoretic description of $\mu$-prolongations, and $\mu$-symmetries of differential equations
• Integration of differential equations by ${\mathcal{C}}^{\infty }$-structures
• ${\mathcal{C}}^{\infty }$-structures in the integration of involutive distributions