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An analytical approach to the theory of electromagnetic waves in nonlinear vacuum is developed. The evolution of the pulse is governed by a system of nonlinear wave vector equations. Exact solution with own angular momentum in form of a…
Electron motion in an oblique shock wave is studied by means of a one-dimensional, relativistic, electromagnetic, particle simulation code with full ion and electron dynamics. It is found that an oblique shock can produce electrons with…
The wave kinetic equation has become an important tool in different fields of physics. In particular, for surface gravity waves, it is the backbone of wave forecasting models. Its derivation is based on the Hamiltonian dynamics of surface…
This paper is devoted to studying a type of logarithmic wave equation in non-cylindrical domains. Firstly, by the penalty method, we prove the existence of weak solutions to such kind of equations. Secondly, different from the dissipative…
In graphene, where the electron-electron scattering is dominant, electrons collectively act as a fluid. This hydrodynamic behaviour of charge carriers leads to exciting nonlinear phenomena such as solitary waves and shocks, among others. In…
The interaction of two counter-propagating electromagnetic waves in a vacuum is analyzed within the framework of the Heisenberg-Euler formalism in quantum electrodynamics. The nonlinear electromagnetic wave in the quantum vacuum is…
We calculate the gravitational form factors of the electron at one loop in quantum electrodynamics, decomposing these into contributions from the electron and photon parts of the energy-momentum tensor. Ultraviolet divergences are removed…
We consider a model dissipative quantum-mechanical system realized by coupling a quantum oscillator to a semi-infinite classical string which serves as a means of energy transfer from the oscillator to the infinity and thus plays the role…
We study the electromagnetic field equations on an arbitrary quantum curved background in the semiclassical approximation of Loop Quantum Gravity. The effective interaction hamiltonian for the Maxwell and gravitational fields is obtained…
In this paper we analyze how radiation effects influence the correlation functions, the excess energy, and in turn the electron correlation energy of the quantized electron gas at temperature $T=0$. To that aim we resort to a statistical…
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…
It is considered the Dirac equation with two different four-potentials of the plane electromagnetic waves. We derive the equation for the wave function which is generalized form of the Volkov equation. We find the solutions of the Dirac…
By using the quantum hydrodynamic and Maxwell equations, we derive nonlinear electron-magnetohydrodynamic (MHD), Hall-MHD, and dust Hall-MHD equations for dense quantum magnetoplasmas. The nonlinear equations include the electromagnetic,…
We postulate a new nonlinear generalization of the Dirac equation for an electron. Basic properties of the new equation are considered.
A nonlinear extension of Schr\"odinger's wave equation is proposed that ensures non-signaling by keeping linear the evolution of \textit{coordinate-diagonal} elements of the density matrix. The equation contains a negative kinetic energy…
The basic equations governing propagation of electromagnetic and gravitational waves in vacuum are nonlinear. As a consequence photon-photon interaction as well as photon-graviton interaction can take place without a medium. However,…
The emission of $\nu\bar\nu$ pairs off electrons in a polarized ultra-intense electromagnetic (e.g.\ laser) wave field is analyzed. We elaborate on the significance of non-linear electrodynamics effects (i.e., multi-photon processes) and…
We provide a compendium of the quantum mechanical equations for photon emission rates, photon absorption cross sections, and photon scattering cross sections. For each case, the different equations that apply for discrete or continuous…
We compare different gravitational-wave extraction methods used in three-dimensional nonlinear simulations against linear simulations of perturbations of spherical spacetimes with matter. We present results from fully general-relativistic…
Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order (O[(v/c)^5] and O[(v/c)^7] beyond Newtonian order), we derive the equations of motion for binary…