Related papers: A special non-linear equation of mathematical phys…
Wave propagation of field disturbances is ubiquitous. The electromagnetic and gravitational are cousin theories in which the corresponding waves play a relevant role to understand several related physical. It has been established that small…
A new nonlinear electromagnetic wave mode in a magnetized plasma is predicted. Its existence depends on the interaction of an intense circularly polarized electromagnetic wave with a plasma, where quantum electrodynamical photon--photon…
An electromagnetic wave (EMW) interacting with the moving singularity of the charged particle flux undergoes the reflection and absorption as well as frequency change due to Doppler effect and nonlinearity. The singularity corresponding to…
By solving Maxwell's equations the exact dispersion equation for electromagnetic waves propagating in a layered coaxial ferrite line is obtained. In particular the analytical consideration is carried out for a simpler case of complete…
It is substantiated that spin is a notion associated with the group of internal symmetry that is tightly connected with the geometrical structure of spacetime. The wave equation for the description of the particles with spin one half is…
We consider a (2+1)-dimensional mechanical system with the Lagrangian linear in the torsion of a light-like curve. We give Hamiltonian formulation of this system and show that its mass and spin spectra are defined by one-dimensional…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional power-law dependence in a wide frequency range can be described by differential equations with time derivatives of noninteger order. We…
The relativistic quantum equation is proposed for the complex wave function, which has the meaning of a probability amplitude. The Lagrangian formulation of the proposed theory is developed. The problem of spreading of a wave packet in an…
In this paper it is shown that the equations of electric field lines of an arbitrarily moving charged particle in the general case are reduced to homogeneous, linear differential equations with variable coefficients. For trajectories where…
We consider the motion of a nonrelativistic electron in the field of two strong monochromatic light waves propagating counter to each other. The wave function of the electron is obtained by using a quasiclassical approximation and…
We establish the classical wave equation for a particle formed of a massless oscillatory elementary charge generally also traveling, and the resulting electromagnetic waves, of a generally Doppler-effected angular frequency $\w$, in the…
Interaction of a charged particle in a static magnetic background, i.e., a Landau system with circularly polarised gravitational wave (GW) is studied quantum mechanically in the long wavelength and low velocity limit. We quantize the…
We consider radial solutions to the Cauchy problem for the linear wave equation with a small short-range electromagnetic potential (the "square version" of the massless Dirac equation with a potential) and zero initial data. We prove two a…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the diffraction problem of a plane wave on…
Propagation of the extremely short electromagnetic pulse in non-linear dielectric media without the slowly varying envelope approximation is discussed. The models under consideration take into account both resonant and not-resonant…
The idea of wave mechanics leads naturally to assume the well-known relation $E=\hbar \omega $ in the specific form $H=\hbar W$, where $H$ is the classical Hamiltonian of a particle and $W$ is the dispersion relation of the sought-for wave…
A formula for the electromagnetic (EM) field in the medium, in which many small perfectly conducting particles of an arbitrary shape are distributed, is derived.
We demonstrate that a sufficiently smooth solution of the relativistic Euler equations that represents a dynamical compact liquid body, when expressed in Lagrangian coordinates, determines a solution to a system of non-linear wave equations…
We propose a new relativistic Lorentz-invariant spin-noncommutative algebra. Using the Weyl ordering of noncommutative position operators, we build an analogue of the Moyal-Groenewald product for the proposed algebra. The Lagrange function…