Noether's Theorem and Symmetry

• 1. autor: Paliathanasis, Andronikos (auth)
• Kolejni autorzy: Leach, P.G.L (auth)
• Format: Elektroniczne Rozdział
• Język: angielski
• Wydane: MDPI - Multidisciplinary Digital Publishing Institute 2020
• Hasła przedmiotowe: n/a; integrable nonlocal partial differential equations; continuous symmetry; Gauss-Bonnet cosmology; double dispersion equation; optimal systems; viscoelasticity; group-invariant solutions; symmetry reduction; Noether symmetries; roots; modified theories of gravity; invariant; variational principle; action integral; conservation laws; conservation law; Noether operators; quasi-Noether systems; Noether symmetry approach; wave equation; Lagrange anchor; quasi-Lagrangians; Lie symmetry; multiplier method; analytic mechanics; optimal system; spherically symmetric spacetimes; Boussinesq equation; lie symmetries; generalized symmetry; first integral; Noether's theorem; Lie symmetries; nonlocal transformation; energy-momentum tensor; boundary term; first integrals; invariant solutions; FLRW spacetime; Noether operator identity; Kelvin-Voigt equation; symmetries; partial differential equations; systems of ODEs; approximate symmetry and solutions
• Dostęp online: DOAB: download the publication; DOAB: description of the publication

In Noether's original presentation of her celebrated theorem of 1918, allowances were made for the dependence of the coefficient functions of the differential operator which generated the infinitesimal transformation of the Action Integral upon the derivatives of the dependent variable(s), the so-called generalized, or dynamical, symmetries. A similar allowance is to be found in the variables of the boundary function, often termed a gauge function by those who have not read the original paper. This generality was lost after texts such as those of Courant and Hilbert or Lovelock and Rund confined attention to only point transformations. In recent decades, this diminution of the power of Noether's Theorem has been partly countered, in particular, in the review of Sarlet and Cantrijn. In this Special Issue, we emphasize the generality of Noether's Theorem in its original form and explore the applicability of even more general coefficient functions by allowing for nonlocal terms. We also look at the application of these more general symmetries to problems in which parameters or parametric functions have a more general dependence upon the independent variables.