Related papers: On periodic solutions and attractors for the Maxwe…
A novel unified Hamiltonian approach is proposed to solve Maxwell-Schrodinger equation for modeling the interaction between classical electromagnetic (EM) fields and particles. Based on the Hamiltonian of electromagnetics and quantum…
For Maxwell's equations with nonlinear polarization we prove the existence of time-periodic breather solutions travelling along slab or cylindrical waveguides. The solutions are TE-modes which are localized in space directions orthogonal to…
We consider a natural class of time-periodic infinite-dimensional nonlinear Hamiltonian systems modelling the interaction of a classical mechanical system of particles with a scalar wave field. When the field is defined on a space torus…
We consider a minimally coupled scalar field with a monomial potential and a perfect fluid in flat FLRW cosmology. We apply local and global dynamical systems techniques to a new three-dimensional dynamical systems reformulation of the…
The aim of this paper is to describe the structure of global attractors for non-autonomous difference systems of equations with recurrent (in particular, almost periodic) coefficients. We consider a special class of this type of systems…
Discrete Ginzburg-Landau (DGL) equations with non-local nonlinearities have been established as significant inherently discrete models in numerous physical contexts, similar to their counterparts with local nonlinear terms. We study two…
Generalizing of the Maxwell field to nonlinear electrodynamics theories, we look for the magnetic solutions. In initial approximation these models give the usual linear electrodynamics. We consider a suitable metric and investigate the…
We derive the global dynamic properties of the mMKG system (Maxwell coupled with a massive Klein-Gordon scalar field) with a general, unrestrictive class of data, in particular, for Maxwell field of arbitrary size, and by a gauge…
We consider a Large Eddy Simulation model for a homogeneous incompressible Newtonian fluid in a box space domain with periodic boundary conditions on the lateral boundaries and homogeneous Dirichlet conditions on the top and bottom…
We present a general solution of the coupled Einstein-Maxwell field equations (without the source charges and currents) in three spacetime dimensions. We also admit any value of the cosmological constant. The whole family of such…
We present an elementary proof of existence of infinite family of time-periodic solutions to the one-dimensional nonlinear cubic wave equation with Dirichlet boundary conditions. It relies on the first order perturbative expansion and uses…
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…
Lie groups involving potential symmetries are applied in connection with the system of magnetohydrodynamic equations for incompressible matter with Ohm's law for finite resistivity and Hall current in cylindrical geometry. Some…
We derive relativistic Maxwell-Bloch equations for potential applications in astronomical environments, where various radiative processes are known to occur, including the maser action and Dicke's superradiance. We show that for both…
The Maxwell-Boltzmann moment system can be seen as a particular case of a mathematically more general moment system proposed by Machado in Ref [1]. This last moment system, whose integral generating form and a suggested continuous…
We discuss the radiation problem of total reflection for a time-harmonic generalized Maxwell system in a non-smooth exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards…
An asymptotic investigation of monochromatic electromagnetic fields in a layered periodic medium is carried out under the assumption that the wave frequency is close to the frequency of a stationary point of the dispersion surface. We find…
The Euler-Maxwell system as a hydrodynamic model for plasma physics to describe the dynamics of the compressible electrons in a constant charged non-moving ion background is studied. The global smooth flow with small amplitude is…
In this article we study the long-time behaviour of a system of nonlinear Partial Differential Equations (PDEs) modelling the motion of incompressible, isothermal and conducting modified bipolar fluids in presence of magnetic field. We…
In this paper, around a global smooth irrotational solution to the classical isentropic compressible Euler-Poisson system, we construct classical solutions to the one-species relativistic Vlasov-Maxwell-Boltzmann system on any finite time…