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We carry out a group-theoretical study of the pair of nonlinear Schr\"{o}dinger equations describing the propagation of waves in nonlinear birefringent optical fibers. We exploit the symmetry algebra associated with these equations to…
Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…
The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical…
Stellar pulsations in rotating relativistic stars are reviewed. Slow rotation approximation is applied to solving the Einstein equations. The rotational effects on the non-axisymmetric oscillations are explicitly shown in the polar and…
We present the derivation of generic equations describing the long gravity waves in incompressible fluid with decaying effect. We show that in this theory the only restriction to the surface deviation is connected with the stability…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
Last year physicists in Europe have measured the velocity of the neutrinos particles. They found the neutrinos moving faster than the speed of light in vacuum. This result means that Einstein's relativity principle and its consequences in…
In contrast to electrodynamics, Einstein's gravitation equations are not invariant with respect to a wide class of the mapping of field variables which leave equations of motion of test particles in a given coordinate system invariant. It…
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic…
A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…
We discuss image formation in gravitational lensing systems using wave optics. Applying the Fresnel-Kirchhoff diffraction formula to waves scattered by a gravitational potential of a lens object, we demonstrate how images of source objects…
Using the Einstein gravitation theory we show how to obtain the basic equations which predict the gravitational waves. This paper was written to graduate and post-graduate students of Physics. We deduce the equations didactically following…
We study two counter-propagating electromagnetic waves in the vacuum within the framework of the Heisenberg-Euler formalism in quantum electrodynamics. We show that the non-linear field equations decouple for ordinary wave case and can be…
Wave effects can be important for the gravitational lensing of gravitational waves. In such a case, wave optics must be used in stead of geometric optics. We consider a plane wave entering a lens object and solve numerically the wave…
Einstein's General Theory of Relativity predicts that accelerating mass distributions produce gravitational radiation, analogous to electromagnetic radiation from accelerating charges. These gravitational waves have not been directly…
Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…
In this article, I present an elementary introduction to the theory of gravitational waves. This article is meant for students who have had an exposure to general relativity, but, results from general relativity used in the main discussion…
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…
Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic behavior at infinity is established. Some generalizations to nonautonomous radial…
The point symmetry group is studied for the generalized Webster-type equation describing non-linear acoustic waves in lossy channels with variable cross sections. It is shown that, for certain types of cross section profiles, the admitted…