In this paper the Maxwell field theory is considered on a closed and orientable Riemann surface of genus h > 1. The solutions of the Maxwell equations corresponding to nontrivial values of the first Chern class are explicitly constructed for any metric in terms of the prime form.

Jason Frank1, Benedict Leimkuhler2 and Keith W. Myerscough3,† 1Mathematical Institute, Utrecht University, PO Box 80010, 3508 TA Utrecht, The Netherlands 2School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Edinburgh EH9 3JZ, UK 3Centrum Wiskunde and Informatica, PO Box 94079, 1090 GB Amsterdam, The Neth...

It is shown how the gauge of the “regular finite initial value problem at spacelike infinity” can be used to construct a certain type of estimates for the Maxwell field propagating on a Schwarzschild background. These estimates are constructed with the objective of obtaining information about the smoothness near spacelike and null infinity of a wide class of solutions to the Maxwell equations.

We prove the existence and uniqueness of non-trivial stable solutions to Landau-Lifshitz-Maxwell equations with Dirichlet boundary condition for large anisotropies and small domains, where the domains are non-simply connected.

We consider a class of inverse source problems for the parabolic approximation to the Maxwell equations using a Bayesian approach.

It is shown that the Maxwell's equations for surface electromagnetic TM waves, propagating along the plane boundary between two nonlinear dielectrics with arbitrary diagonal tensor of dielectric permittivity, depending on |E|, can be integrated in quadratures.

We study the asymptotic regime for the relativistic Vlasov-Maxwell-FokkerPlanck system which corresponds to a mean free path small compared to the Debye length, chosen as an observation length scale, combined to a large thermal velocity assumption. We are led to a convection-diffusion equation, where the convection velocity is obtained by solving a Poisson equation. The analysis is performed in...

Split-step procedures have previously been used successfully in a number of situations, e.g. for Hamiltonian systems, such as certain nonlinear wave equations. In this study, we note that one particular way to write the 3-D Maxwell’s equations separates these into two parts, requiring in all only the solution of six uncoupled 1-D wave equations. The approach allows arbitrary orders of accuracy ...

The relation between the two most important in mathematical physics first order systems of partial differential equations is among those topics which attract attention because of their general, even philosophical significance but at the same time do not offer much for the solution of particular problems concerning physical models. The Maxwell equations can be represented in a Dirac like form in...