Noether's Theorem and Symmetry
Paliathanasis, Andronikos
Noether's Theorem and Symmetry - MDPI - Multidisciplinary Digital Publishing Institute 2020 - 1 electronic resource (186 p.)
Open Access
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.
Creative Commons
English
books978-3-03928-235-7 9783039282340 9783039282357
10.3390/books978-3-03928-235-7 doi
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
Noether's Theorem and Symmetry - MDPI - Multidisciplinary Digital Publishing Institute 2020 - 1 electronic resource (186 p.)
Open Access
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.
Creative Commons
English
books978-3-03928-235-7 9783039282340 9783039282357
10.3390/books978-3-03928-235-7 doi
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