Related papers: Nonlinear Electrodynamics without Birefringence
In a series of papers, Quesne and Tkachuk (J. Phys. A: Math. Gen. \textbf{39}, 10909 (2006); Czech. J. Phys. \textbf{56}, 1269 (2006)) presented a $D+1$-dimensional $(\beta,\beta')$-two-parameter Lorentz-covariant deformed algebra which…
We define an iterative procedure to obtain a non-abelian generalization of the Born-Infeld action. This construction is made possible by the use of the severe restrictions imposed by kappa-symmetry. We have calculated all bosonic terms in…
Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian…
The relativistic Boltzmann equation in bounded domains has been widely used in physics and engineering, for example, Tokamak devices in fusion reactors.In spite of its importance, there has, to the best of our knowledge, been no…
The concept of self-dual supersymmetric nonlinear electrodynamics is generalized to a curved superspace of N = 1 supergravity, for both the old minimal and the new minimal versions of N = 1 supergravity. We derive the self-duality equation,…
Cosmic birefringence is the process that rotates the plane of polarization by an amount, $\alpha$, as photons propagate through free space. Such an effect arises in parity-violating extensions to the electromagnetic sector, such as the…
A theory for nonlinear optics of semiconductors in the presence of an intense terahertz electric field is constructed based on the double-line Feynman diagrams, in which the nonperturbative effect of the intense terahertz field is fully…
Converging cylindrical electromagnetic fields in vacuum have been shown (E. I. Zababakhin, M. N. Nechaev, {\it Soviet Physics JETP}, {\bf 6}, 345 (1958)) to exhibit amplitude "cumulation". It was found that the amplitude of self-similar…
In this paper, we deal with the electrostatic Born-Infeld equation \begin{equation}\label{eq:BI-abs} \tag{$\mathcal{BI}$} \left\{ \begin{array}{ll} -\operatorname{div}\left(\displaystyle\frac{\nabla \phi}{\sqrt{1-|\nabla \phi|^2}}\right)=…
This paper studies the dynamical behavior near a new family of explicit self-similar solutions for the one dimensional Born-Infeld equation. This quasilinear scalar field equation arises from nonlinear electromagnetism, as well as branes in…
We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…
An investigation is performed of the Lorentz-violating electrodynamics extracted from the renormalizable sector of the general Lorentz- and CPT-violating standard-model extension. Among the unconventional properties of radiation arising…
We found Lagrangian action which describes spinning particle on the base of non-Grassmann vector and involves only one auxiliary variable. It provides the right number of physical degrees of freedom and yields generalization of the Frenkel…
We analyze the behavior of shock waves in nonlinear theories of electrodynamics. For this, by use of generalized Hadamard step functions of increasing order, the electromagnetic potential is developed in a series expansion near the shock…
We prove existence and uniqueness of mild solutions to Sobolev type fractional nonlocal dynamic equations in Banach spaces. The Sobolev nonlocal condition is considered in terms of a Riemann-Liouville fractional derivative. A Lagrange…
We consider the bending of light by nonlinear electrodynamics when the magnetic field $B$ exceeds the critical value $B_{\rm c}$. Using the index of refraction derived from the analytic series representation in one-loop effective action of…
The linear electromagnetic response of a uniform electron gas to a longitudinal electric field is determined, within the self-consistent-field theory, by the linear polarizability and the Lindhard dielectric function. Using the same…
We investigate gauge-invariant nonlinear electrodynamics in the Pleba\'nski first-order Hamiltonian formulation, taking the single-invariant potential $\hat V(P)$ as the primary object. Our focus is on the existence of stable…
We prove a Caffarelli--Kohn--Nirenberg inequality in the hyperbolic space. For a semilinear elliptic equation involving the associated weighted Laplace--Beltrami operator, we establish variationally the existence of positive radial…
We study nonlinear vacuum electrodynamics in a first-order formulation proposed by Pleba\'nski. By applying a Dirac constraint analysis, we derive an effective Hamiltonian, together with the equations of motion. We show that there exists a…