Related papers: On inverse problems in electromagnetic field in cl…
In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic Newton equation with an external potential $V$, $V\in C^2$. Using known results,…
We consider the inverse scattering problem at fixed and sufficiently large energy for the nonrelativistic and relativistic Newton equation in $\R^n$, $n \ge 2$, with a smooth and short range electromagnetic field $(V,B)$. Using results of…
We consider the multidimensional Newton-Einstein equation in static electromagnetic field $$\eqalign{\dot p = F(x,\dot x), F(x,\dot x)=-\nabla V(x)+{1\over c}B(x)\dot x,\cr p={\dot x \over \sqrt{1-{|\dot x|^2 \over c^2}}}, \dot p={dp\over…
We define scattering data for the relativistic Newton equation in an electric field $-\nabla V\in C^1(\R^n,\R^n)$, $n\ge 2$, and in a magnetic field $B\in C^1(\R^n,A_n(\R))$ that decay at infinity like $r^{-\alpha-1}$ for some $\alpha\in…
We consider the multidimensional (nonrelativistic) Newton equation in a static electromagnetic field $$\ddot x = F(x,\dot x), F(x,\dot x)=-\nabla V(x)+B(x)\dot x, \dot x={dx\over dt}, x\in C^2(\R,\R^n),\eqno{(*)}$$ where $V \in…
We transform an inverse scattering problem to be an interior transmission problem. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of…
We study the inverse scattering problem for electric potentials and magnetic fields in $\ere^d, d\geq 3$, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from…
The following inverse problem is discussed. A static electromagnetic field generated by a limited system of charges and currents is supposed to be known with its first derivatives at a point somewhere far from the system. This allows to…
Inverse scattering and spectral one-dimensional problems are discussed systematically in a self-contained way. Many novel results, due to the author are presented. The classical results are often presented in a new way. Several highlights…
We inquire into classical and quantum laws of motion for the point charge sources in the nonlinear Maxwell-Born-Infeld field equations of classical electromagnetism in flat and curved Einstein spacetimes.
We study an inverse scattering problem at fixed energy for radial magnetic Schr{\"o}dinger operators on R^2 \ B(0, r\_0), where r\_0 is a positive and arbitrarily small radius. We assume that the magnetic potential A satisfies a gauge…
We apply a particular form of the inverse scattering theory to turbulent magnetic fluctuations in a plasma. In the present note we develop the theory, formulate the magnetic fluctuation problem in terms of its electrodynamic turbulent…
In this paper we consider the inverse scattering problem at a fixed energy for the Schr\"odinger equation with a long-range potential in $\ere^d, d\geq 3$. We prove that the long-range part can be uniquely reconstructed from the leading…
Standard formulae of classical electromagnetism for the forces between electric charges in motion derived from retarded potentials are compared with those obtained from a recently developed relativistic classical electrodynamic theory with…
The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…
In a $U(1)_{\star}$-noncommutative (NC) gauge field theory we extend the Seiberg-Witten (SW) map to include the (gauge-invariance-violating) external current and formulate - to the first order in the NC parameter - gauge-covariant classical…
A formulation of classical electrodynamics on an energy-momentum background of constant, non-zero curvature is given. The procedure consists of taking the formulation of standard electrodynamics in the energy-momentum representation, and…
We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…
In this paper we study an inverse boundary value problem for Maxwell's equations. The goal is to reconstruct perturbations in the refractive index of the medium inside an object from the knowledge of the tangential trace of an electric…
The inverse scattering problem of the three-dimensional Schroedinger equation is considered at fixed scattering energy with spherically symmetric potentials. The phase shifts determine the potential therefore a constructive scheme for…