相关论文: From Maxwell Stresses to Nonlinear Field Equations

Instead of a linear system of equations for a free electromagnetic field, we propose a nonlinear system of equations. The classical electrodynamics is preseved. The appeared solutions (the electromagnetic fields) having photon properties.…

We review our recent work leading to steady-state solutions of the semiclassical (Maxwell-Bloch) equations of a laser. These are coupled non-linear partial differential equations in space and time which have previously been solved either by…

The Coulomb force, established in the rest frame of a source-charge $Q$, when transformed to a new frame moving with a velocity $\vec{V}$ has a form $\vec{F}= q\vec{{E}} + q\vec{v} \times \vec{{B}}$, where $\vec{{E}}=\vec{E}'_\parallel +…

We consider the question of linear instability of an equilibrium of the Relativistic Vlasov-Maxwell (RVM) System that has a strong magnetic field. Standard instability results deal with systems where there are fewer particles with higher…

The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…

We formulate a geometric framework that allows to study momentum and energy transport in non-relativistic systems. It amounts to coupling of the non-relativistic system to the Newton-Cartan geometry with torsion. The approach generalizes…

By applying the nonlinear Legendre transform to the continuity equation, this paper derives exact solutions to the Schr\"odinger equation and the equations of continuum mechanics. A generalized Maxwell distribution has been used as the…

We extend the fully non-linear and exact cosmological perturbation equations in a Friedmann background universe to include the background curvature. The perturbation equations are presented in a gauge ready form, so any temporal gauge…

A new solution with constant torsion is derived using the field equations of f(T). Asymptotic forms of energy density, radial and transversal pressures are shown to meet the standard energy conditions, i.e., weak and null energy conditions…

We define an abstract nonlinear elliptic system, admitting a variational structure, and including the vortex equations for some Maxwell-Chern-Simons gauge theories as special cases. We analyze the asymptotic behavior of its solutions, and…

We demonstrate how to derive Maxwell's equations, including Faraday's law and Maxwell's correction to Amp\`ere's law, by generalizing the description of static electromagnetism to dynamical situations. Thereby, Faraday's law is introduced…

Using relativistic kinetic theory, we study spherically symmetric, static equilibrium configurations of a collisionless Maxwell-Boltzmann gas with non-standard self-interactions, modelled by an effective one--particle force. The resulting…

The generalized Maxwell equations are considered which include an additional gradient term. Such equations describe massless particles possessing spins one and zero. We find and investigate the matrix formulation of the first order of…

Based on the Vlasov-Maxwell equations describing the self-consistent nonlinear beam dynamics and collective processes, the evolution of an intense sheet beam propagating through a periodic focusing field has been studied. In an earlier…

Starting with the MacDowell-Mansouri formulation of gravity with a $SO(4,1)$ gauge group, we introduce new parameters into the action to include the non-dynamical Holst term, and the topological Nieh-Yan and Pontryagin classes. Then, we…

The regularized Maxwell theory is a recently discovered theory of non-linear electrodynamics that admits many important gravitating solutions within the Einstein theory. Namely, it was originally derived as the unique non-linear…

In this paper we discuss global existence of the solution of the Maxwell and Newton system of equations, describing the interaction of a rigid charge distribution with the electromagnetic field it generates. A unique solution is proved to…

We construct global-in-time classical solutions to the nonlinear Vlasov-Maxwell system in a three-dimensional half-space beyond the vacuum scattering regime. Our approach combines the construction of stationary solutions to the associated…

Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or…

We study gravitational properties of vacuum energy by erecting a geometry on the stress-energy tensor of vacuum, matter and radiation. Postulating that the gravitational effects of matter and radiation can be formulated by an appropriate…