Related papers: Asymptotic conservation laws in field theory
In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant…
The motion of an incompressible fluid in Lagrangian coordinates involves infinitely many symmetries generated by the left Lie algebra of group of volume preserving diffeomorphisms of the three dimensional domain occupied by the fluid.…
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…
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 characterize all cases when a certain natural generalization of the Infeld--Rowlands equation admits nontrivial local conservation laws of any order, and give explicit form of these conservation laws modulo trivial ones. Furthermore, we…
Based on investigations of the fundamental properties of the generalized Einstein Lagrangian density for a gravitational system, the theoretical foundations of the modified Einstein field equations and the Lorentz and Levi-Civita…
Basic features of the conservation laws in the Hamiltonian approach to the Poincar\'e gauge theory are presented. It is shown that the Hamiltonian is given as a linear combination of ten first class constraints. The Poisson bracket algebra…
Under suitable assumptions on the boundary conditions, it is shown that there is a bijective correspondence between equivalence classes of asymptotic reducibility parameters and asymptotically conserved n-2 forms in the context of…
Using a manifestly invariant Lagrangian density based on Clebsch fields and suitable for geophysical fluid dynamics, the conservation of mass, entropy, momentum and energy, and the associated symmetries are investigated. In contrast, it is…
We report a new energy conservation law for time-harmonic electromagnetic fields, which is valid for an arbitrary medium. In contrast to the well-established Poynting theorem for time-harmonic fields, the real part of the new energy…
The Lagrangian formulation of field theory does not provide any universal energy-momentum conservation law in order to analize that in gravitation theory. In Lagrangian field theory, we get different identities involving different stress…
A large class of first order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating function is constructed. The conserved…
The generalized Kawahara equation $u_t=a(t) u_{xxxxx} +b(t)u_{xxx} +c(t)f(u) u_x$ appears in many physical applications. A complete classification of low-order conservation laws and point symmetries is obtained for this equation, which…
In this work we study a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations. We find conservation laws by using the multipliers method of Anco and Bluman which does…
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…
Electromagnetic fields of an accelerated charge are derived from the first principles using Coulomb's law and the relativistic transformations. The electric and magnetic fields are derived first for an instantaneous rest frame of the…
In the present work, we formulate a generalization of the Noether Theorem for action-dependent Lagrangian functions. The Noether's theorem is one of the most important theorems for physics. It is well known that all conservation laws,…
Conservation principles are essential to describe and quantify dynamical processes in all areas of physics. Classically, a conservation law holds because the description of reality can be considered independent of an observation…
A complete classification of all low-order conservation laws is carried out for a system of coupled semilinear wave equations which is a natural two-component generalization of the nonlinear Klein-Gordon equation. The conserved quantities…
In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous…