Related papers: Conservation laws and covariant equations of motio…
We use the Lagrange-Noether methods to derive the conservation laws for models in which matter interacts nonminimally with the gravitational field. The nonminimal coupling function can depend arbitrarily on the gravitational field strength.…
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
We study general metric-affine theories of gravity in which the metric and connection are the two independent fundamental variables. In this framework, we use Lagrange-Noether methods to derive the identities and the conservation laws that…
A construction of conservation laws and conserved quantities for perturbations in arbitrary metric theories of gravity is developed. In an arbitrary field theory, with the use of incorporating an auxiliary metric into the initial Lagrangian…
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…
We review the Lagrangian formulation of Noether symmetries (as well as "generalized Noether symmetries") in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called "Natural Theories" and "Gauge-Natural…
It's well known that Noether symmetries lead to the conservation laws. Conserved quantities are constructed out of generator of the symmetry - invariant Hamiltonian vector field. Considering more general class of vector fields -…
We analyse the conservation laws in the gauge gravity theory which are derived for the general class of gravitational models with the action invariant under the local Poincare and the diffeomorphism group. The consistent Noether-Lagrange…
Conservation laws of a class of time-dependent damped nonlinear multidimensional wave equations are derived by Noether's theorem. For arbitrary nonzero damping coefficient and nonlinear interaction term, its infinitesimal variational…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
For difference variational problems on lattice, this paper presents a relation between divergence variational symmetries and conservation laws for the associated Euler-Lagrange system provided by Noether's theorem. This hence inspires us to…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
In Lagrangian mechanics, Noether conservation laws including the energy one are obtained similarly to those in field theory. In Hamiltonian mechanics, Noether conservation laws are issued from the invariance of the Poincare-Cartan integral…
Noether's calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the…
Noether's theorem and the invariances of the Willmore functional are used to derive conservation laws that are satisfied by the critical points of the Willmore energy subject to generic constraints. We recover in particular previous results…
In the present paper geometric aspects of relationship between non-Noether symmetries and conservation laws in Hamiltonian systems is discussed. It is shown that integrals of motion associated with continuous non-Noether symmetry are in…
A class of generalized Galileon cosmological models, which can be described by a point-like Lagrangian, is considered in order to utilize Noether's Theorem to determine conservation laws for the field equations. In the…
We present a covariant derivation of the equations of motion for test bodies for a wide class of gravitational theories with nonminimal coupling, encompassing a general interaction via the complete set of 9 parity-even curvature invariants.…
Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave…
Using the fact that extremum of variation of generalized action can lead to the fractional dynamics in the case of systems with long-range interaction and long-term memory function, we consider two different applications of the action…