Related papers: A special non-linear equation of mathematical phys…
There are important differences between the nonrelativistic and relativistic description of electron beams. The orbital angular momentum quantum number cannot be used to specify the wave functions in the relativistic case. In this Letter we…
It is shown that two ways of the description of the 1/2-spin precession in a circularly polarized electromagnetic wave: on the basis of the Bargmann-Michel-Telegdi equation and on the basis of the Dirac equation with Pauli term give the…
The parametrized Dirac wave equation represents position and time as operators, and can be formulated for many particles. It thus provides, unlike field-theoretic Quantum Electrodynamics (QED), an elementary and unrestricted representation…
We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative…
We derive the modified Dirac equation for an electron undergos an influence of the standard model interaction with the nuclear matter. The exact solutions for this equation and the electron energy spectrum in matter are obtained. This…
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…
We combine Maxwell's equations with Eulers's equation, related to a velocity field of an immaterial fluid, where the density of mass is replaced by a charge density. We come out with a differential system able to describe a relevant…
Electromagnetic particle simulation model has been formulated and verified for nonlinear processes of lower hybrid (LH) waves in fusion plasmas. Electron dynamics is described by the drift kinetic equation using either kinetic momentum or…
This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first…
Closed-form, normalizable solutions of Dirac's equation propagating within a semi-infinite cylindrical waveguide are obtained in terms of ordinary and modified Bessel functions. These relativistic wave packets induce quantum backflow on a…
A new nonlinear Schroedinger equation is obtained explicitly from the fractal Brownian motion of a massive particle with a complex-valued diffusion constant. Real-valued energy (momentum) plane wave and soliton solutions are found in the…
A new model of nonlinear electrodynamics with three parameters is suggested and investigated. It is shown that if the external constant magnetic field presents the phenomenon of vacuum birefringence takes place. The indexes of refraction…
The nonlinear dynamics of the free surface of an ideal dielectric liquid in a strong electric field is studied. The equation for the evolution of surface electrohydrodynamic waves is derived in the approximation of small surface-slope…
From the simple Lagrangian the equations of motion for the particle with spin are derived. The spin is shown to be conserved on the particle world-line. In the absence of a spin the equation coincides with that of a geodesic. The equations…
The paper deals with the one possible mechanism of the pulsar radio emission, i.e., with the collective curvature radiation of the relativistic particle stream moving along the curved magnetospheric magnetic field lines. It is shown that…
It is known that a nonlinear Schr\"odinger equation describes the self-modulation of a large amplitude circularly polarized wave in relativistic electron-positron plasmas in the weakly and strongly magnetized limits. Here, we show that such…
In a frame of quasi-crystal approximation the dispersion equations are obtained for the wave vector of a coherent electromagnetic wave propagating in a media which contains a random set of parallel dielectric cylinders with possible…
The problem of propagating nonlinear acoustic waves is considered; the solution to which, both with and without damping, having been obtained to-date starting from the Navier-Stokes-Duhem equations together with the continuity and thermal…
We describe a new class of exact square integrable solutions of the Pauli and Dirac equation in rotating electromagnetic fields. Solutions obtained by putting equations in the stationary form with help of a coordinate transformation…
The analysis of nonlinear interaction of transversal electromagnetic field with collisionless plasma is carried out. Formulas for calculation electric current in collisionless plasma with arbitrary degree of degeneration of electronic gas…