相关论文: Finite Energy Superluminal Solutions of Maxwell Eq…
In this paper we prove the existence of infinitely many small energy solution of a semilinear Schrodinger equation via the dual form of the generalized fountain theorem. This equation is with periodic potential and concave-convex…
Exact solutions of the relativistic many-body problem are presented
A systematic procedure to derive exact solutions of the associated Lame equation for an arbitrary value of the energy is presented. Supersymmetric transformations in which the seed solutions have factorization energies inside the gaps are…
Whether the smooth solution of the multi-dimensional viscous compressible fluids will blow-up in finite time has always been a chanllenging problem. In the recent work\cite{FM}, Merle et al. proved that there are smooth solutions to the 2D…
We propose a new class of fundamental solutions for the numerical analysis of boundary value problems for the Maxwell equations. We prove completeness of systems of such fundamental solutions in appropriate Sobolev spaces on a smooth…
In a gravitational field, we analyze the Maxwell equations, the correponding electromagnetic wave and continuity equations. A particular solution for parellel electric and magnetic fields in a gravitational background is presented. These…
We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…
Using octonions, more specifically, using a 4 x 4 matrix representation of octonions obtained with the help of algebraic properties of quaternions, we obtain the fully symmetric Maxwell's equations (Maxwell's equations with electric and…
Analytical solutions to the wave equation in spheroidal coordinates in the short wavelength limit are considered. The asymptotic solutions for the radial function are significantly simplified, allowing scalar spheroidal wave functions to be…
The paper gives a comprehensive study of infinite-energy solutions and their long-time behavior for semi-linear weakly damped wave equations in $\mathbb{R}^3$ with quintic nonlinearities. This study includes global well-posedness of the…
This paper aims to show that making use of Newton's view on equations of motion of a physical system and of the Maxwell stress tensor we come to a natural nonlinearization of Maxwell equations in vacuum making use only of nonrelativistic…
The distributional form of the Maxwell-Vlasov equations are formulated. Submanifold distributions are analysed and the general submanifold distributional solutions to the Vlasov equations are given. The properties required so that these…
In this lecture we will show some properties of a singularity-free solution to Einstein's equations and its accordance with some theorems dealing with singularities. We will also discuss the implications of the results.
Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions'…
We discuss the use of a class of exact finite energy solutions to the vacuum source-free Maxwell equations as models for multi- and single cycle laser pulses in classical interaction with relativistic charged point particles. These compact…
We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is…
In this paper we study the following nonlinear Maxwell's equations \\ $\varepsilon \E_{t}+\sigma(x,|\E|)\E= \g \vh +\F,\, \vh_{t}+\g \E=0$, where $\sigma(x,s)$ is a monotone graph of $s$. It is shown that the system has a unique weak…
In the case where the charge of the particle is small compared to its mass, we describe the asymptotics of the Lorentz-Maxwell equation for any finite-energy data. As time goes to infinity, we prove that the speed of the particle converges…
The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in vacuum is investigated within the matrix formalism. The matrix form of electrodynamics includes three real 4 \times 4 matrices. Within the…
For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational…