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Uniqueness results are established for time-independent finite-energy electromagnetic fields which solve the nonlinear Maxwell--Born--Infeld equations in boundary-free space under the condition that either the charge or current density…

All nonlinear extensions of the source-free Maxwell equations preserving both SO(2) electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalisation of Born-Infeld…

A nonlinear charged version of the (2+1)-anti de Sitter black hole solution is derived. The source to the Einstein equations is a Born-Infeld electromagnetic field, which in the weak field limit becomes the (2+1)-Maxwell field. The obtained…

A perturbation series solution is constructed in terms of Airy functions for a nonlinear two-point boundary-value problem arising in an established model of steady electrodiffusion in one dimension, for two ionic species carrying equal and…

The Cho-Maison monopole provides a monopole solution of the electroweak field equations, but possesses an infinite classical energy due to the Maxwell form of the hypercharge sector. Motivated by string-inspired effective field theories, we…

We derive the essential space-time spectrum of the Maxwell equations in linear isotropic inhomogeneous media together with the corresponding essential modes. These modes represent the collapse of the electromagnetic field into a single…

Nonlinear Maxwell equations are written up to the third-power deviations from a constant-field background, valid within any local nonlinear electrodynamics including QED with a Euler-Heisenberg (EH) effective Lagrangian. The linear electric…

We present a new class of exact self-similar solutions possessing cylindrical or spherical symmetry in Born-Infeld theory. A cylindrically symmetric solution describes the propagation of a cylindrical electromagnetic disturbance in a…

The non-linear second order Born-Infeld equation is reduced to a simpler first order complex equation, which can be trivially solved for the coordinates as functions of the field. Each solution is determined by the choice of a holomorphic…

The classical Maxwell--Born--Infeld field equations coupled with a Hamilton--Jacobi law of point charge motion are partially quantized by coupling the Hamilton-Jacobi phase function with an amplitude function, which combines with the phase…

The Abelian Born-Infeld classical non-linear electrodynamic has been used to investigate the electric and magnetostatic fields generated by a point-like electrical charge at rest in an inertial frame. The results show a rich internal…

Stationary circularly symmetric solutions of General Relativity with negative cosmological constant coupled to the Maxwell field are analyzed in three spacetime dimensions. Taking into account that the fall-off of the fields is slower than…

Exact finite-energy solutions to the nonlinear governing equations of the Born-Infeld theory of electrodynamics, describing continuous distributions of electric, magnetic, and dyonic charge sources, in both classical and generalized…

The electric potential and the electromagnetic field for a linearly accelerated Born-Infeld charged particle are obtained in an inertial frame by a method that can, in principle, be applied to any electromagnetic theory. The method is based…

We extend the classical results on the symmetry inheritance of the canonical electromagnetic fields, described by the Maxwell's Lagrangian, to a much wider class of models, which include those of the Born-Infeld, power Maxwell and the…

We obtain convergent power series representations for Bloch waves in periodic high-contrast media. The material coefficient in the inclusions can be positive or negative. The small expansion parameter is the ratio of period cell width to…

Two-dimensional Born-Infeld electrostatic fields behaving as the superposition of two point-like charges in the linearized (Maxwellian) limit are worked out by means of a non-holomorphic mapping of the complex plane. The changes underwent…

We consider the Maxwell equation in the exterior of a very slowly rotating Kerr black hole. For this system, we prove the boundedness of a positive definite energy on each hypersurface of constant $t$. We also prove the convergence of each…

Calculations of the ground state of inhomogeneous many-electron systems involve a solving of the Poisson equation for Coulomb potential and the Schroedinger equation for single-particle orbitals. Due to nonlinearity and complexity this set…

We present a description of the electromagnetic field for propagation invariant beams using scalar potentials. Fundamental dynamical quantities are obtained: the energy density, the Poynting vector and the Maxwell stress tensor. As an…