Related papers: Noether's Theorem on Time Scales
A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both…
We prove a version of the variational Euler-Lagrange equations valid for functionals defined on Fr\'echet manifolds, such as the spaces of sections of differentiable vector bundles appearing in various physical theories.
Noether's theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: (i) it is not applicable to dynamics wherein the system interacts…
The article concerns the problem if a~given system of differential equations is identical with the Euler--Lagrange system of an~appropriate variational integral. Elementary approach is applied. The main results involve the determination of…
We use Noether symmetry approach to find spherically symmetric static solutions of the non-minimally coupled electromagnetic fields to gravity. We construct the point-like Lagrangian under the spherical symmetry assumption. Then we…
We apply Noether's theorem to show how the invariances of conservative systems are broken for nonconservative systems, in the variational formulation of Galley. This formulation considers a conservative action, extended by the inclusion of…
We investigate splitting-type variational problems with some linear growth conditions. For balanced solutions of the associated Euler-Lagrange equation we receive a result analogous to Bernstein's theorem on non-parametric minimal surfaces.…
Ertel's potential vorticity theorem is essentially a clever combination of two conservation principles. The result is a conserved scalar $q$ that accurately reflects possible vorticity values that fluid parcels can possess and acts as a…
This article examines the analytic solutions of isotropic spacetime with the minimal coupling of scalar field and matter in the context of energy-momentum squared gravity. The scalar field includes quintessence and phantom dark energy…
Usually we consider the symmetry of action as the symmetry of the theory, however, in the Keplar problem the scaling symmetry existing in equa tion of motion is not the ones for action. It changes the multiplicative c onstant of action and…
We study in this paper the continuous and discrete Euler-Lagrange equations arising from a quadratic lagrangian. Those equations may be thought as numerical schemes and may be solved through a matrix based framework. When the lagrangian is…
We derive Euler-Lagrange equations for the topology optimization of decay rate in 3-d lossy optical cavities. This leads to a new class of time-harmonic differential or integro-differential equations, which can be written as nonlinear…
This review is dedicated to some modern applications of the remarkable paper written in 1918 by E. Noether. On a single paper, Noether discovered the crucial relation between symmetries and conserved charges as well as the impact of gauge…
When discussing consequences of symmetries of dynamical systems based on Noether's first theorem, most standard textbooks on classical or quantum mechanics present a conclusion stating that a global continuous Lie symmetry implies the…
We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional…
Noether's first and second theorems both imply conserved currents that can be identified as an energy-momentum tensor (EMT). The first theorem identifies the EMT as the conserved current associated with global spacetime translations, while…
We extend the second Noether theorem to fractional variational problems which are invariant under infinitesimal transformations that depend upon $r$ arbitrary functions and their fractional derivatives in the sense of Caputo. Our main…
Using the short time existence of the Calabi flow, we prove that any extremal Kaehler metric on a product toric variety is a product extremal Kaehler metric.
It is known that corresponding to each isometry there exist a conserved quantity. It is also known that the Lagrangian of the line element of a space is conserved. Here we investigate the possibility of the existence of "new" conserved…
We consider Noether symmetries of the equations defined by the sections of characteristic line bundles of nondegenerate 1-forms and of the associated perturbed systems. It appears that this framework can be used for time-dependent systems…