Related papers: Energy Content of Colliding Plane Waves using Appr…
A generalization of the KP equation involving higher-order dispersion is studied. This equation appears in several physical applications. As new results, the Lie point symmetries are obtained and used to derive conservation laws via…
Backgrounds are pervasive in almost every application of general relativity. Here we consider the Lagrangian formulation of general relativity for large perturbations with respect to a curved background spacetime. We show that Noether's…
Plane electromagnetic and gravitational waves interact with particles in such a way as to cause them to oscillate not only in the transverse direction but also along the direction of propagation. The electromagnetic case is usually shown by…
In this review we consider the quadratic Metric-Affine Gauge gravity Lagrangian, which contains all the algebraic invariants up to quadratic order in torsion, nonmetricity and curvature. The goal will be to collect the known exact solutions…
An exact analytical model of the process of collision and nonlinear interaction of gravitational and/or electromagnetic soliton wave and strong non-soliton electromagnetic traveling wave of arbitrary profile propagating in the expanding…
A class of generally nonlinear dynamical systems is considered, for which the Lagrangian is represented as a sum of homogeneous functions of the displacements and their derivatives. It is shown that an energy partition as a single relation…
The known exact solutions of Einstein's vacuum field equations modeling the gravitational fields of pure gravitational radiation involve wave fronts which are either planar or roughly spherical. We describe a scheme designed to check…
It has been argued that the energy content in time varying spacetimes can be obtained by using the approximate Lie symmetries of the geodesics equations in that spacetime. When applied to cylindrical gravitational waves, it gives a…
A system of equations, describing the evolution of electromagnetic fields, is introduced and discussed. The model is strictly related to Maxwell's equations. As a matter of fact, the Lagrangian is the same, but the variations are subjected…
We use Noether symmetry approach to find spherically symmetric static solutions of the non-minimally coupled electromagnetic fields to gravity. We construct the point-like Lagrangian under the spherical symmetry assumption. Then we…
The paper considers the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. The inviscid, thermally non-conducting medium is modeled by a polytropic gas. The equations are examined for symmetries and…
Recently a simple solution of the vacuum Einstein-Maxwell field equations was given describing a plane electromagnetic shock wave sharing its wave front with a plane gravitational impulse wave. We present here an exact solution of the…
In this paper, we study the solitary wave and the Cauchy problem for Half-wave-Schr\"{o}dinger equations in the plane. First, we show the existence and orbital stability of the ground states. Secondly, we prove that traveling waves exist…
We consider the collisions of plane gravitational and electromagnetic waves with distinct wavefronts and of arbitrary polarizations in a Minkowski background. We first present a new, completely geometric formulation of the characteristic…
Symmetries and, in particular, Cartan (Noether) symmetries and conserved quantities (conservation laws) are studied for the multisymplectic formulation of first and second order Lagrangian classical field theories. Noether-type theorems are…
We study the head-on collision of linearly polarized, high frequency plane gravitational waves and their electromagnetic counterparts in the Einstein-Maxwell theory. The post-collision space-times are obtained by solving the vacuum…
Using the ``composite harmonic mapping method," we construct exact solutions for cylindrically symmetric gravitational and electromagnetic waves within the Einstein-Maxwell system, focusing on the conversion dynamics between these types of…
In this paper we construct a new solution which represents Pollard-like three-dimensional nonlinear geophysical internal water waves. The Pollard-like solution includes the effects of the rotation of Earth and describes the internal water…
We discuss some Lagrangian and presymplectic models concerning test particles in electromagnetic and gravitational fields, with the aim of describing an upper bound to the acceleration. Some models are based on the relativistic phase space…
We present the first results in a new program intended to make the best use of all available technologies to provide an effective understanding of waves from inspiralling black hole binaries in time for imminent observations. In particular,…