Related papers: Nonuniqueness of nonrunaway solutions of Abraham-L…
We consider the massless nonlinear Dirac (NLD) equation in $1+1$ dimension with scalar-scalar self-interaction $\frac{g^2}{2} (\bar{\Psi} \Psi)^2$ in the presence of three external electromagnetic potentials $V(x)$, a potential barrier, a…
In this paper, a novel approach for resolution of the Abraham-Minkowski debate is proposed, in which the principle of relativity is used to uniquely determine the light momentum formulation for a plane wave in a moving non-dispersive…
Current classical theory of radiation reaction has several deficiencies such as "runaway solutions" and violation of causality. The Landau-Lifshitz approximation to the exact equation introduced by Lorentz, Abraham and Dirac is widely used,…
Similar to introduce the Lorentz condition in the motion equation of electromagnetic field, the restriction condition is introduced in the motion equations of non-Ablian gauge fields so that the equations are simplified greatly and their…
Up until now, a consistent causal theory of point charged particles (for example electrons) interacting with electromagnetic field is not known. The well-known problem is that the standard Lorentz force alone (in the case of point…
We discuss the unstable character of the solutions of the Lorentz-Dirac equation and stress the need of methods like order reduction to derive a physically acceptable equation of motion. The discussion is illustrated with the paradigmatic…
The dynamics and radiation of ultrarelativistic electrons in strong counterpropagating laser beams are investigated. Assuming that the particle energy is the dominant scale in the problem, an approximate solution of classical equations of…
A Rayleigh wave is a type of surface wave that propagates in the boundary of an elastic solid with traction (or Neumann) boundary conditions. Since the 1980s much work has been done on the problem of constructing a leading term in an…
We present a study of planar physical solutions to the Lorentz-Dirac equation in a constant electromagnetic field. In this case, we reduced the Lorentz-Dirac equation to the one second order differential equation. We obtained the…
The Lorentz-Abraham-Dirac equations (LAD) may be the most commonly accepted equation describing the motion of a classical charged particle in its electromagnetic field. However, it is well known that they bare several problems. In…
The averaged resonant equations of motion for the planar circular restricted three-body problem are solved on the linearization basis taking into account also non-gravitational effects. The averaged resonant equations are derived from…
The interaction of a multi-Petawatt, pancake-shaped laser pulse with an unmagnetized plasma is studied analytically and numerically in the regime of fully relativistic electron jitter velocities and in the context of the laser wakefield…
The Lorentz-Abraham-Dirac (LAD) equation has proved valuable in describing the motion of radiating electric charges but suffers from runaway, pre-acceleration and other ambiguities. The usual scheme is problematic because of locality, which…
We describe the structure of solutions of the kinetic Fokker-Planck equations in domains with boundaries near the singular set in one-space dimension. We study in particular the behaviour of the solutions of this equation for inelastic…
In this survey we report on some recent results related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations. We establish qualitative results on the existence, nonexistence or the uniqueness of…
We take the viewpoint that the physically acceptable solutions of the Lorentz--Dirac equation for radiation back-reaction are actually determined by a second order equation of motion, the self-force being given as a function of spacetime…
The exact solution of the Dirac equation and the spectrum of electron quasi-energies in a superposition of the field of a circularly polarized electromagnetic wave and a homogeneous magnetic field parallel to the direction of wave…
A relatively simple model problem where a single electron moves in two relativistically-strong obliquely intersecting plane wave-packets is studied using a number of different numerical solvers. It is shown that, in general, even the most…
We investigate the nonlinear interaction between a relativistically strong laser beam and a plasma in the quantum regime. The collective behavior of the electrons is modeled by a Klein-Gordon equation, which is nonlinearly coupled with the…
A model for the dynamics of a classical point charged particle interacting with higher order jet fields is introduced. In this model, the dynamics of the charged particle is described by an implicit ordinary second order differential…