TY  - GEN
AU  - Paliathanasis,Andronikos
AU  - Leach,P.G.L.
TI  - Noether's Theorem and Symmetry
SN  - books978-3-03928-235-7
PY  - 2020///
PB  - MDPI - Multidisciplinary Digital Publishing Institute
KW  - n/a
KW  - integrable nonlocal partial differential equations
KW  - continuous symmetry
KW  - Gauss-Bonnet cosmology
KW  - double dispersion equation
KW  - optimal systems
KW  - viscoelasticity
KW  - group-invariant solutions
KW  - symmetry reduction
KW  - Noether symmetries
KW  - roots
KW  - modified theories of gravity
KW  - invariant
KW  - variational principle
KW  - action integral
KW  - conservation laws
KW  - conservation law
KW  - Noether operators
KW  - quasi-Noether systems
KW  - Noether symmetry approach
KW  - wave equation
KW  - Lagrange anchor
KW  - quasi-Lagrangians
KW  - Lie symmetry
KW  - multiplier method
KW  - analytic mechanics
KW  - optimal system
KW  - spherically symmetric spacetimes
KW  - Boussinesq equation
KW  - lie symmetries
KW  - generalized symmetry
KW  - first integral
KW  - Noether's theorem
KW  - Lie symmetries
KW  - nonlocal transformation
KW  - energy-momentum tensor
KW  - boundary term
KW  - first integrals
KW  - invariant solutions
KW  - FLRW spacetime
KW  - Noether operator identity
KW  - Kelvin-Voigt equation
KW  - symmetries
KW  - partial differential equations
KW  - systems of ODEs
KW  - approximate symmetry and solutions
N1  - Open Access
N2  - 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
UR  - https://mdpi.com/books/pdfview/book/2056
UR  - https://directory.doabooks.org/handle/20.500.12854/54710
ER  -