相关论文: Solving the characteristic initial value problem f…

Since the main open problem of contemporary physics is to find a unified description of the four interactions, we present a possible scenario which, till now only at the classical level, is able to englobe experiments ranging from…

We present the exact solution to the linearized Maxwell equations in space-time slightly curved by a gravitational wave. We show that in general, even dealing with a first-order theory in the strength of the gravitational field, the…

We focus our attention, once again, on the Klein--Gordon and Dirac equations with a plane-wave field. We recall that for the first time a set of solutions of these equations was found by Volkov. The Volkov solutions are widely used in…

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,…

In this paper, we study the problem of the nonlinear interaction of impulsive gravitational waves for the Einstein vacuum equations. The problem is studied in the context of a characteristic initial value problem with data given on two null…

Motivated by the problem of the evolution of bulk gravitational waves in Randall-Sundrum cosmology, we develop a characteristic numerical scheme to solve 1+1 dimensional wave equations in the presence of a moving timelike boundary. The…

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…

We consider a scalar Hamiltonian nonlinear wave equation formulated on networks; this is a non standard problem because these domains are not locally homeomorphic to any subset of the Euclidean space. More precisely, we assume each edge to…

Gravitational waves from astrophysical sources can interact with background electromagnetic fields, giving rise to distinctive and potentially detectable electromagnetic signatures. In this paper, we study such interactions for far-field…

Applying a simple harmonic map method to the cylindrically symmetric Einstein-Maxwell system, we obtain exact solutions representing strong nonlinear interaction between gravitational waves and electromagnetic waves in the case without any…

We are concerned with hyperbolic systems of order-one linear PDEs originated on non-characteristic manifolds. We put forward a simple but effective method of transforming such initial conditions to standard initial conditions (i.e. when the…

This brief note wants to bring to attention that the formulation of physically reasonable initial-boundary value problems for wave equations in Lorentzian space-times is not unique, i.e., that there are inequivalent such formulations that…

The dynamics of metric perturbations is explored in the gravity theory with anomaly-induced quantum corrections. Our first purpose is to derive the equation for gravitational waves in this theory on the general homogeneous and isotropic…

For a one-dimensional mildly quasilinear wave equation given in the upper half-plane, we consider the Cauchy problem. The initial conditions have discontinuity of the first kind at one point. We construct the solution using the method of…

We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a…

We study the equations of motion for a barotropic fluid in spherical symmetric flow. Making use of the Riemann invariants we consider the characteristic form of these equations. In a first part, we show that the resulting constraint…

Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the…

The relativistic Vlasov-Maxwell system of plasma physics is considered with initial data on a past light cone. This characteristic initial value problem arises in a natural way as a mathematical framework to study the existence of solutions…

When two non-interacting plane impulsive gravitational waves undergo a head-on collision, the vacuum interaction region between the waves after the collision contains backscattered gravitational radiation from both waves. The two systems of…

We formulate a new approach to solving the initial value problem of the shallow water-wave equations utilizing the famous Carrier-Greenspan transformation [G. Carrier and H. Greenspan, J. Fluid Mech. 01, 97 (1957)]. We use a Taylor series…