相关论文: Nonuniqueness of nonrunaway solutions of Abraham-L…
It is shown that the nonlinear Ermakov-Milne-Pinney equation $\rho^{\prime\prime}+v(x)\rho=a/\rho^3$ obeys the property of covariance under a class of transformations of its coefficient function. This property is derived by using…
We prove conditional weak-strong uniqueness of the potential Euler solution for external flow around a smooth body in three space dimensions, within the class of viscosity weak solutions with the same initial data. Our sufficient condition…
In this work, we investigate the influence of torsion, Aharonov-Bohm flux, and external magnetic fields on the linear and nonlinear optical properties of a confined quantum system. The confinement potential is not assumed a priori, but…
Solitary waves of nonlinear Dirac, Maxwell-Dirac and Klein-Gordon-Dirac equations are considered. We prove that the energy-momentum relation for solitary waves coincides with the Einstein energy-momentum relation for point particles.
It is known that Lorentz covariance fixes uniquely the current and the associated guidance law in the trajectory interpretation of quantum mechanics for spin particles. In the non-relativistic domain this implies a guidance law for the…
We present equations of motion for charged particles using balanced equations, and without introducing explicitly divergent quantities. This derivation contains as particular cases some well known equations of motion, as the Lorentz-Dirac…
We study Dirichlet-type problems for the simplest third-order linear dispersive PDE, often referred to as the Airy equation. Such problems have not been extensively studied, perhaps due to the complexity of the spectral structure of the…
In classical electrodynamics for rotating with variable angular velocity charged rigid sphere are found: the exact values of electromagnetic fields, the flux of radiating energy and the exact integral equation of rotation including the…
The cubic nonlinear Helmholtz equation with third and fourth order dispersion and non-Kerr nonlinearity like the self steepening and the self frequency shift is considered. This model describes nonparaxial ultrashort pulse propagation in an…
Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation…
We are concerned with the study of the system of coupled equations of motion for a system of two-level atoms interacting with a single-mode field in the laser cavity on resonance. The passage from the equation of motion to the Lorenz…
We consider particles emanating from a source point inside an interval in one-dimensional space and passing through detectors situated at the endpoints of the interval that register their arrival time. Unambiguous measurements of arrival or…
When a solution to the Cauchy problem for nonlinear dispersive equations is obtained by a fixed point argument using auxiliary function spaces, it is non-trivial to ensure uniqueness of solutions in a natural space such as the class of…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
We formulate the Lorentz-Dirac equation in the plane wave and in the Dirac delta-function pulse. The discussion on the relation of the Dirac delta-function to the ultrashort laser pulse is involved.
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \mapsto \infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the…
Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary…
Classically encountered problem of acceleration runaway in radiative motion of a charged-particle is addressed by considering the criterion of minimum radiation loss under optimum displacement in variationally referred dynamic course in…
This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general…
An axisymmetric space-localized solution of nonlinear electrodynamics is considered as massive charged particle with spin and magnetic moment. The appropriate solution for nonlinear electrodynamics with ring singularity is investigated. In…