Related papers: Nonlinear Maxwell Theory and Electrons in Two Dime…
We study standing wave solutions to nonlinear Schr{\"o}dinger equations, on a manifold with a rotational symmetry, which transform in a natural fashion under the group of rotations. We call these vortex solutions. They are higher…
Despite the success of Maxwell's electromagnetism in the description of the electromagnetic interactions on small scales, we know very little about the behaviour of electromagnetic fields on cosmological distances. Thus, it has been…
Within the framework of the homogeneous non-linear Boltzmann equation, we present a new analytic method, without the intrinsic limitations of existing methods, for obtaining asymptotic solutions. This method permits extension of existing…
The (2 + 1)-dimensional gauge model describing two complex scalar fields that interact through a common Abelian gauge field is considered. It is shown that the model has a soliton solution that describes a system consisting of a vortex and…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…
In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to…
We consider nontopological first-order solitons arising from a gauged $CP(2)$ model in the presence of the Maxwell term multiplied by a nontrivial dielectric function. We implement the corresponding first-order scenario by proceeding the…
The vortex-like solution to the non-linear field equations in a two-dimensional SU(2) gauge theory with the Chern-Simons mass term is found at high temperature. It is derived from the effective Lagrangian including the leading order finite…
The Duffin-Kemmer form of massless vector field (Maxwell field) is extended to the case of arbitrary pseudo-Riemannian space-time in accordance with the tetrad recipe of Tetrode-Weyl-Fock-Ivanenko. In this approach, the Maxwell equations…
We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…
The nonlinear propagation of internal gravity waves in the weakly ionized, incompressible Earth's ionosphere is studied using the fluid theory approach. Previous theory in the literature is advanced by the effects of the terrestrial…
We consider the electromagnetic field in the presence of polarizable point dipoles. In the corresponding effective Maxwell equation these dipoles are described by three dimensional delta function potentials. We review the approaches…
This paper summarizes the motivations and results obtained so far in the frame of a particular non-linearization of Classical Electrodynamics, which was called Extended Electrodynamics. The main purpose pursued with this non-linear…
One-particle eigenstates and eigenvalues of two-dimensional electrons in the strong magnetic field with short range impurity and impurities, cosine potential, boundary potential, and periodic array of short range potentials are obtained by…
In this chapter, we review the Ra\~{n}ada field line solutions of Maxwell's equations in the vacuum, which describe a topologically non-trivial electromagnetic field, as well as their relation with the knot theory. Also, we present a…
Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. We show that this singular behavior does not occur for a class of nonlinear generalizations of…
We demonstrate that spatially inhomogeneous defocusing nonlinear landscapes with the nonlinearity coefficient growing toward the periphery as [1+abs(r)]**a support one- and two-dimensional fundamental and higher-order bright solitons, as…
Theories of non-linear electrodynamics naturally describe deviations from Maxwell's theory in the strong field regime. Among these, of special interest is the recently discovered ModMax electrodynamics, which is a unique 1-parametric…
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…
For a system of equations describing one-dimensional nonlinear oscillations in a magnetoactive plasma, we study the effect of a constant magnetic field on the breaking of oscillations. For the nonrelativistic case, a criterion for the…