Related papers: A special non-linear equation of mathematical phys…
This article is focused on a multidimensional nonlinear variational wave equation which is the Euler-Lagrange equation of a variational principle arising form the theory of nematic liquid crystals. By using the method of characteristics, we…
Conventional descriptions of transverse waves in an elastic solid are limited by an assumption of infinitesimally small gradients of rotation. By assuming a linear response to variations in orientation, we derive an exact description of a…
The equation is considered for a composite scalar particle with polarizabilities in an external quantized electromagnetic plane wave. This equation is reduced to a system of equations for infinite number of interacting oscillators. After…
In the present paper it is shown that the Maxwell theory can be finely represented in the matrix form of Dirac's equation, if the Dirac wave function is identified with the electromagnetic wave by defined way. It seems to us, that such…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…
Last year physicists in Europe have measured the velocity of the neutrinos particles. They found the neutrinos moving faster than the speed of light in vacuum. This result means that Einstein's relativity principle and its consequences in…
The nonlinear interaction between intense laser light and a quantum plasma is modeled by a collective Dirac equation coupled with the Maxwell equations. The model is used to study the nonlinear propagation of relativistically intense laser…
Using the thin-layer approach, we derive the effective equation for the electromagnetic wave propagating along a space curve. We find intrinsic spin-orbit, extrinsic spin-orbit and extrinsic orbital angular momentum and intrinsic orbital…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
From non-linear theory of electromagnetism, suggested in (physics/9801031), follows that non-relativistic equation for scalar potential of electron in the field of nuclei is equivalent to respective Schr\"odinger equation. For mass and…
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…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonmagnetic, linearly polarized, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the…
Maxwell's equations and the Dirac equation are the first-order differential relativistic wave equation for electromagnetic waves and electronic waves respectively. Hence, there is a notable similarity between these two wave equations, which…
We discuss the dynamics of a classical spinless quantum particle carrying electric charge and constrained to move on a non singular static surface in ordinary three dimensional space in the presence of arbitrary configurations of time…
The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…
Fully non-linear, plane-symmetric exact solutions of the Einstein equations describing the scattering of gravitational and electromagnetic waves have existed for many years. For these closed-form solutions to be found, idealized wave…
In this work we provide a novel class of degenerate solutions to the Dirac equation for massive particles, where the rotation of the spin of the particles is synchronized with the rotation of the magnetic field of the wave-like…
This article devoted to relativistic dynamics of a charged massive particle in an electroscalar field. It represents a continuation of paper [1] where the authors constructed a non-relativistic theory which describes transverse…
Here is constructed a heuristic, first-order differential equation for the electromagnetic field in the vacuum, based on a phenomenological \textsl{ad hoc} argument. The formal similarity between this \textsl{ad hoc} wave equation and the…