In this paper we introduce a new method to study the influence of thermal conduction and viscous processes in anisotropic gravitational collapse. To this end we employ the HJR method to solve the Einstein equations. The Maxwell-Cattaneo type transport equations are used to find the temperature and bulk and shear viscous pressures. Under some conditions Maxwell-Cattaneo transport equations compl...

Relativistic definition of the phase of the electromagnetic field, involving two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to extend our previous study @I. Bialynicki-Birula, Z. BialynickaBirula, and C. Śliwa, Phys. Rev. A 61, 032110 ~2000!# of the motion of vortex lines embedded in the solutions of wave equations from Schrödinger wave mechanics to Maxwell theory. I...

We consider the Boltzmann equations for mixtures of Maxwell gases. It is shown that in certain limiting case the equations admit self-similar solutions that can be constructed in explicit form. More precisely, the solutions have simple explicit integral representations. The most interesting solutions have finite energy and power like tails. This shows that power like tails can appear not just f...

Cylindrical nonlinear optics is a burgeoning research area which describes cylindrical electromagnetic wave propagation in nonlinear media. Finding new exact solutions for different types of nonlinearity and inhomogeneity to describe cylindrical electromagnetic wave propagation is of great interest and meaningful for theory and application. This paper gives exact solutions for the cylindrical n...

Propagation of extremely short pulses of electromagnetic field (electromagnetic spikes) is considered in the framework of the total Maxwell-Duffing model where anharmonic oscillators with cubic nonlinearities (Duffing model) represent the material medium and wave propagation is governed by the 1-d bidirectional Maxwell equations. This system of equations has a one parameter family of exact anal...

In this paper the authors extend their previous work on Boundary Perturbation methods for scattering calculations from families of diffraction gratings to three dimensions and the full vector electromagnetic Maxwell equations. This extension is non-trivial in both its algorithmic implementation (not only are new terms added to the recursions, but also the full, coupled, vector Maxwell equations...