Noether's Theorem and Symmetry

Edited by
March 2020
186 pages
  • ISBN978-3-03928-234-0 (Paperback)
  • ISBN978-3-03928-235-7 (PDF)

This book is a reprint of the Special Issue Noether's Theorem and Symmetry that was published in

Biology & Life Sciences
Chemistry & Materials Science
Computer Science & Mathematics
Physical Sciences
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.
  • Paperback
© 2020 by the authors; CC BY-NC-ND license
wave equation; spherically symmetric spacetimes; lie symmetries; roots; optimal systems; invariant solutions; n/a; Noether symmetry approach; FLRW spacetime; action integral; variational principle; first integral; modified theories of gravity; Gauss-Bonnet cosmology; Noether’s theorem; action integral; generalized symmetry; first integral; invariant; nonlocal transformation; boundary term; conservation laws; analytic mechanics; Noether’s theorem; generalized symmetry; energy-momentum tensor; Lagrange anchor; viscoelasticity; Kelvin-Voigt equation; Lie symmetries; optimal system; group-invariant solutions; conservation laws; multiplier method; continuous symmetry; symmetry reduction; integrable nonlocal partial differential equations; symmetries; conservation laws; Noether operator identity; quasi-Noether systems; quasi-Lagrangians; Lie symmetry; conservation law; double dispersion equation; Boussinesq equation; systems of ODEs; Noether operators; Noether symmetries; first integrals; partial differential equations; approximate symmetry and solutions