We find the Lax pair for a system of reduced Maxwell–Bloch equations that describes the propagation of twocomponent extremely short electromagnetic pulses through the medium containing two-level quantum particles with arbitrary dipole moments.

The numerical solution of very large 3D electromagnetic field problems are challenging for various applications in the industry. In this paper, we propose a nonoverlapping domain decomposition approach for solving the 3D Maxwell equations on MIMD computers, based on a mixed variational formulation. It is especially well adapted for the solution of the Vlasov-Maxwell equations, widely used to si...

Abstract Matrix representations of the Maxwell equations are well-known. However, all these representations lack an exactness or/and are given in terms of a pair of matrix equations. We present a matrix representation of the Maxwell equation in presence of sources in a medium with varying permittivity and permeability. It is shown that such a representation necessarily requires 8×8 matrices and...

Dissipative effects in electromagnetism on macroscopic scales are examined by coarse-graining the microscopic Maxwell equations with respect to time. We illustrate a procedure to derive the dissipative effects on the macroscopic scale by using a Green-Kubo type expression in terms of the microscopic fluctuations and the correlations between them. The resulting macroscopic Maxwell equations are ...

A fully discrete nite element method is used to approximate the electric eld equation derived from Maxwell equations in three dimensional polyhedral domains. Optimal energy-norm error estimates are achieved for general Lipschitz polyhedral domains. Optimal L 2-norm error estimates are obtained for convex polyhedral domains. R esum e On r esout, dans un domaine poly edrique, les equations de Max...

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 solutions can be a distributional source to Maxwell’s equations are analysed and it is shown that a sufficient condition is that spacetime be globally hyperboli...