相关论文: Nonuniqueness of nonrunaway solutions of Abraham-L…

We study a Boussinesq system in a bounded domain with an outlet boundary portion where fluid can leave or re-enter. On this boundary part, we consider a do-nothing condition for the fluid flow, and a new artificial condition for the heat…

We study the problems of uniqueness for Hardy-H\'enon parabolic equations, which are semilinear heat equations with the singular potential (Hardy type) or the increasing potential (H\'enon type) in the nonlinear term. To deal with the…

The onset of the Rayleigh-Benard instability in a horizontal fluid layer is investigated by assuming the fluid as a binary mixture and the concentration buoyancy as the driving force. The focus of this study is on the anomalous diffusion…

Starting with the Dirac equation for an electron in a constant electromagnetic background on a noncommutative (NC) plane, we obtain a gauge invariant description of the system. Surprisingly, the dynamics of the system is dictated by the…

The Lorentz-Dirac radiation reaction formula predicts that the position shift of a charged particle due to the radiation reaction is of first order in acceleration if it undergoes a small acceleration. A semi-classical calculation shows…

We reanalyze the problem of a 1D Dirac single particle colliding with the electrostatic potential step of height $V_{0}$ with a positive incoming energy that tends to the limit point of the so-called Klein energy zone, i.e., $E\rightarrow…

We study the behavior of solitary-wave solutions of some generalized nonlinear Schr\"odinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing…

Uniqueness results are established for time-independent finite-energy electromagnetic fields which solve the nonlinear Maxwell--Born--Infeld equations in boundary-free space under the condition that either the charge or current density…

Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…

The Landau-Lifshitz equation is considered as an approximation of the Abraham-Lorentz-Dirac equation. It is derived from the Abraham-Lorentz-Dirac equation by treating radiation reaction terms as a perturbation. However, while the…

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 systems with overdamped dynamics, the Lorentz force reduces the diffusivity of a Brownian particle in the plane perpendicular to the magnetic field. The anisotropy in diffusion implies that the Fokker-Planck equation for the probabiliy…

A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…

We study a conformally invariant equation involving the Dirac operator and a non-linearity of convolution type. This non-linearity is inspired from the conformal Einstein-Dirac problem in dimension 4. We first investigate the compactness,…

The anomalous velocity deviation in the osculating planetary flyby attracts enough attention as a problem of General Relativity. In connection of rotating weak field massive source the Lense Thirring metric is diagonalized to find the…

While the Landau-Lifshitz equation, which describes classical radiation reaction, can be solved exactly and analytically for a charged particle accelerated by a plane electromagnetic wave, no such solutions are available for quantum…

The self-conjugate Dirac Hamiltonian is obtained in the Kerr-Newman field. A transition is implemented to a Schr\"odinger-type relativistic equation. For the case where the angular and radial variables are not separated, the method of…

The ``Jackiw-Nair'' non-relativistic limit of the relativistic anyon equations provides us with infinite-component wave equations of the Dirac-Majorana-Levy-Leblond type for the ``exotic'' particle, associated with the two-fold central…

We investigate the solutions to the Lorentz-Dirac equation and show that its solution flow has a structure identical to the one of renormalization group flows in critical phenomena. The physical solutions of the Lorentz-Dirac equation lie…

The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…