Related papers: Conservation laws and variational structure of dam…
It is shown that the zilch conservation law arises as the Noether current corresponding to a variational symmetry of a duality-symmetric Maxwell Lagrangian. The action of the corresponding symmetry generator on the duality-symmetric…
Nonlinear generalizations of integrable equations in one dimension, such as the KdV and Boussinesq equations with $p$-power nonlinearities, arise in many physical applications and are interesting in analysis due to critical behaviour. This…
We succeed in writing 2-dimensional conformally invariant non-linear elliptic PDE (harmonic map equation, prescribed mean curvature equations...etc) in divergence form. This divergence free quantities generalize to target manifolds without…
Noether's theorem has gained outstanding importance in theoretical particle physics, because it leads to basic conservation laws, such as the conservation of momentum and of angular momentum. Closely related to this theorem, but unnoticed…
The Lagrange, Euler, and Euler-Poincar\'{e} variational principles for the guiding-center Vlasov-Maxwell equations are presented. Each variational principle presents a different approach to deriving guiding-center polarization and…
The dynamics of nonlinear conservation laws have long posed fascinating problems. With the introduction of some nonlinearity, e.g. Burgers' equation, discontinuous behavior in the solutions is exhibited, even for smooth initial data. The…
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…
Emmy Noether proved two deep theorems, and their converses, on the connection between symmetries and conservation laws. Because these theorems are not in the mainstream of her scholarly work, which was the development of modern abstract…
Evidence and results suggesting that a Noether--like theorem for conservation laws in 1D RCA can be obtained. Unlike Noether's theorem, the connection here is to the maximal congruences rather than the automorphisms of the local dynamics.…
Two applications of the Noether method for fluids and plasmas are presented based on the Euler-Lagrange and Euler-Poincare variational principles, which depend on whether the dynamical fields are to be varied independently or not,…
There are many evolution partial differential equations which can be cast into Hamiltonian form. Conservation laws of these equations are related to one-parameter Hamiltonian symmetries admitted by the PDEs. The same result holds for…
The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are reduced to a generalized Euler-Lagrange equation that contains…
The paper considers the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. The inviscid, thermally non-conducting medium is modeled by a polytropic gas. The equations are examined for symmetries and…
There are several formulations of the second law, and they may, in principle, have different domains of validity. Here a simple mathematical theorem is proven which serves as the most general basis for the second law, namely the Thomson…
The exact energy and angular-momentum conservation laws are derived by Noether method for the Hamiltonian and symplectic representations of the gauge-free electromagnetic gyrokinetic Vlasov-Maxwell equations. These gyrokinetic equations,…
A simple characterization of the action of symmetries on conservation laws of partial differential equations is studied by using the general method of conservation law multipliers. This action is used to define symmetry-invariant and…
For the Euler equations governing compressible isentropic fluid flow with a barotropic equation of state (where pressure is a function only of the density), local conservation laws in $n>1$ spatial dimensions are fully classified in two…
We review the formulation of a Lorentz-covariant bispinorial wave function and wave equation for a single photon on a flat background. We show the existence of a 10-dimensional set of conservation laws for this equation, and prove that 8 of…
The time dependent-integrals of motion, linear in position and momentum operators, of a quantum system are extracted from Noether's theorem prescription by means of special time-dependent variations of coordinates. For the stationary case…
The exact momentum conservation laws for the nonlinear gyrokinetic Vlasov-Poisson equations are derived by applying the Noether method on the gyrokinetic variational principle [A. J. Brizard, Phys. Plasmas {\bf 7}, 4816 (2000)]. From the…