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We consider the quadratically semilinear wave equation on R^d, d>=3, equipped with a Riemannian metric. This metric is non-trapping and approaches the Euclidean metric polynomially at infinity. Using Mourre estimates and the Kato theory of…
Original abstract: "We construct periodic solutions of nonlinear wave equations using analytic continuation. The construction applies in particular to Einstein equations, leading to infinite-dimensional families of time-periodic solutions…
Results from helically symmetric scalar field models and first results from a convergent helically symmetric binary neutron star code are reported here; these are models stationary in the rotating frame of a source with constant angular…
We analyse a nonlinear Schr\"odinger equation for the time-evolution of the wave function of an electron beam, interacting selfconsistently through a Hartree-Fock nonlinearity and through the repulsive Coulomb interaction of an atomic…
We provide strong evidence that, up to $99.999\%$ of extremality, Kerr-Newman black holes (KN BHs) are linear mode stable within Einstein-Maxwell theory. We derive and solve, numerically, a coupled system of two PDEs for two gauge invariant…
This paper studies the model of the quantum electrodynamics (QED) of a single nonrelativistic electron due to W. Pauli and M. Fierz and studied further by P. Blanchard. This model exhibits infrared divergence in a very simple context. The…
We obtain two exact solutions of Einstein gravity coupled to nonlinear electrodynamics (NLED) in $(2+ 1)$-dimensional Anti-de Sitter (AdS) spacetime. The solutions are characterized by the mass $M$, angular momentum $J$, cosmological…
We consider a pp-wave symmetric model in the framework of the Einstein-Maxwell-aether-axion theory. Exact solutions to the equations of axion electrodynamics are obtained for the model, in which pseudoscalar, electric and magnetic fields…
Type N spacetimes of the Kundt class are presented as solutions to Einstein's equations sourced by a real scalar field whose equation of motion is conformally invariant and that generalizes the standard conformal scalar field. The specific…
The Wheeler equation has an extension in the Kerr background. It has an exact solution representing a running harmonic wave in the tortoise coordinate. The wave models astrophysical jets in a new light because it collimates along the axis…
We introduce a novel framework for the analysis of linear wave equations on nonstationary asymptotically flat spacetimes, under the assumptions of mode stability and absence of zero energy resonances for a stationary model operator. Our…
At low energies, the quantum wave-like nature of molecular interactions result in unique scattering behavior, ranging from the universal Wigner laws near zero Kelvin to the occurrence of scattering resonances at higher energies. It has…
The nonlinear interaction, due to quantum electrodynamical (QED) effects, between photons is investigated using a wave-kinetic description. Starting from a coherent wave description, we use the Wigner transform technique to obtain a set of…
We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric, E and…
We investigate a new model of nonlinear electromagnetic field coupled with the gravitation field. The black hole solution is obtained possessing the asymptotic Reissner-Nordstr\"om solution. The electric field has the finite value at the…
In general, Maxwell's equations require that a wave of electric field be accompanied by a wave of magnetic field, and vice versa. However, it is possible to have a plane wave in a dielectric medium with electric field E parallel to the wave…
We consider KdV-type equations with $C^1$ nonhomogeneous nonlinearities and small dispersion $\varepsilon$. The first result consists in the conclusion that, in the leading term with respect to $\varepsilon$, the solitary waves in this…
Three dimensional nonlinear wave interactions have been analytically described. The procedure under interest can be applied to three dimensional quasilinear systems of first order, whose hydrodynamic reductions are homogeneous…
We consider the Hamiltonian system consisting of scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subject to an external potential. The stationary solutions of the system are a Coulomb…
In field theory, particles are waves or excitations that propagate on the fundamental state. In experiments or cosmological models one typically wants to compute the out-of-equilibrium evolution of a given initial distribution of such…