Related papers: Analytical solutions for Maxwell-scalar system on …
We prove the existence and uniqueness of global finite energy solutions of the Maxwell-scalar field system in Lorenz gauge on the Einstein cylinder. Our method is a combination of a conformal patching argument, the finite energy existence…
In this paper we establish the existence in low dimensions of solutions to the constraint equations in the case of the conformal system recently proposed by David Maxwell, with the added presence of a scalar field and under suitable…
A modification of the Maxwell equations due to the presence of a gravitational field was formerly proposed for a scalar theory with a preferred reference frame. With this modification, the electric charge is not conserved. The aim of the…
The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the…
We study the quantum mechanical many-body problem of $N$ nonrelativistic electrons interacting with their self-generated classical electromagnetic field and $K$ static nuclei. The system of coupled equations governing the dynamics of the…
We obtain an exact static solution to Einstein-Power-Maxwell (EPM) theory in $(2+1)$ dimensional AdS spacetime, in which the scalar field couples to gravity in a non-minimal way. After considering the scalar potential, a stable system leads…
We study radially symmetric solutions to the 2D Vlasov-Maxwell system and construct solutions that initially possess arbitrarily small $C^k$ norms ($k \geq 1$) for the charge densities and the electric fields, but attain arbitrarily large…
We prove the wellposedness of scalar wave equations on spatially flat universe as a background with nonminimal coupling with the scalar potential turned on by introducing the $k$-order linear energy and the corresponding energy norm. In the…
In this paper, we consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is…
We present a new class of magnetic brane solutions in $(n+1)$-dimensional Brans-Dicke-Maxwell theory in the presence of a quadratic potential for the scalar field. These solutions are neither asymptotically flat nor (anti)-de Sitter. Our…
We study time-independent radially symmetric first-order solitons in a CP(2) model interacting with an Abelian gauge field whose dynamics is controlled by the usual Maxwell term. In this sense, we develop a consistent first-order framework…
We develop a structure-preserving solution framework for the optimal control of the time-dependent Maxwell's equations. Building on a well-posedness theory for a weak form of the forward problem, we first analyze a forward solver that…
We investigate a class of localized, stationary, particular numerical solutions to the Maxwell-Dirac system of classical nonlinear field equations. The solutions are discrete energy eigenstates bound predominantly by the self-produced…
We take as starting point the planar model arising from the dimensional reduction of the Maxwell Electrodynamics with the (Lorentz-violating) Carroll-Field-Jackiw term. We then write and study the extended Maxwell equations and the…
We study the static, spherically symmetric black hole solutions for a non-minimally coupled multi-scalar theory. We find numerical solutions for values of the scalar fields when a certain constraint on the maximal charge is satisfied.…
Stationary circularly symmetric solutions of General Relativity with negative cosmological constant coupled to the Maxwell field are analyzed in three spacetime dimensions. Taking into account that the fall-off of the fields is slower than…
Energy minimizing BPS equations and solutions are obtained for a class of models in Maxwell-scalar theory, where an abelian electric charge is immersed in an effective dielectric of a real scalar field. The first order BPS equations are…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…
We obtain a class of magnetically charged solutions in 2+1 dimensional Einstein - Power - Maxwell theory. In the linear Maxwell limit, such horizonless solutions are known to exist. We show that in 3D geometry, black hole solutions with…
We consider the Maxwell equation in the exterior of a very slowly rotating Kerr black hole. For this system, we prove the boundedness of a positive definite energy on each hypersurface of constant $t$. We also prove the convergence of each…