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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 consider a space-fractional wave equation with a singular mass term depending on the position and prove that it is very weak well-posed. The uniqueness is proved in some appropriate sense. Moreover, we prove the consistency of the very…
We discuss the dynamics of particles in one dimension in potentials that are random both in space and in time. The results are applied to recent optics experiments on Anderson localization, in which the transverse spreading of a beam is…
Propagating, solitary magnetic wave solutions of the Landau-Lifshitz equation with uniaxial, easy-axis anisotropy in thin (two-dimensional) magnetic films are investigated. These localized, nontopological wave structures, parametrized by…
We studied electromagnetic wave propagation in a system that is periodic in both space and time, namely a discrete 2D transmission line (TL) with capacitors modulated in tandem externally. Kirchhoff's laws lead to an eigenvalue equation…
For the $1+1$ dimensional damped stochastic Klein-Gordon equation, we show that random singularities associated with the law of the iterated logarithm exist and propogate in the same way as the stochastic wave equation. This provides…
We consider the Klein--Gordon equation associated with the Laplace--Beltrami operator $\Delta$ on real hyperbolic spaces of dimension $n\!\ge\!2$; as $\Delta$ has a spectral gap, the wave equation is a particular case of our study. After a…
We investigate signal propagation in a quantum field simulator of the Klein-Gordon model realized by two strongly coupled parallel one-dimensional quasi-condensates. By measuring local phononic fields after a quench, we observe the…
We discuss theories in which the standard-model particles are localized on a brane embedded in space-time with large compact extra dimensions, whereas gravity propagates in the bulk. In addition to the ground state corresponding to a…
We present an accurate, stable and efficient solution to the Lippmann-Schwinger equation for electromagnetic scattering in two dimensions. The method is well suited for multiple scattering problems and may be applied to problems with…
Recent interest in the studies of structured states obtained in relativistic electron beams has highlighted the use of two alternative descriptions, each based on a different wavefunction and the related space-time density. Although both…
We obtain sharp decay estimates and asymptotics for small solutions to the one-dimensional Klein-Gordon equation with constant coefficient cubic and spatially localized, variable coefficient cubic nonlinearities. Vector-field techniques to…
A new class of exact solutions of the bound Dirac and bound Klein Gordon equations in non co propagating plane waves is found. The solutions are based on the physical principle of maintaining local gauge invariance in the Furry picture…
We solve Klein-Gordon equation (KGE) in the framework of the real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM). The presented solution is the simplest ever obtained for quaternionic quantum theories, and the…
This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet…
The dynamics of the electroweak phase transition in the early universe has profound implications for cosmology and particle physics. We systematically study the steady-state dynamics of bubble walls in scenarios where the transition is…
In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein-Gordon and Dirac equations in Rindler coordinates with…
The classical free-space solutions of Maxwell's equations for light propagation in one dimension include wave packets of any shape that travel at the speed of light. This includes highly-localised wave packets that remain localised at all…
Computing the properties of the bubble wall of a cosmological first order phase transition at electroweak scale is of paramount importance for the correct prediction of the baryon asymmetry of the universe and the spectrum of gravitational…
Solution of the nonlinear Klein-Gordon equation perturbed by small external force is investigated. The perturbation is represented by finite collections of harmonics. The frequencies of the perturbation vary slowly and pass through the…