Related papers: Klein-Gordon-Maxwell equations in high dimensions
The main purpose of this contribution is to determine physical and geometrical characterizations of whole classes of stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the $(2+1)$-dimensional…
To construct higher-dimensional counterparts of the Kerr-Newman black holes, we consider Einstein's equations sourced by a vector field and a negative cosmological constant. In contrast to the four-dimensional case, the Maxwell's equations…
We obtain the Einstein-Maxwell equations for (2+1)-dimensional static space-time, which are invariant under the transformation $q_0=i\,q_2,q_2=i\,q_0,\alpha \rightleftharpoons \gamma$. It is shown that the magnetic solution obtained with…
In this article, we investigate electrostatic systems with a nonzero cosmological constant on compact manifolds with boundary. We establish new geometric properties for electrostatic manifolds in higher dimensions, extending previous…
The main result of this paper is the proof that there are local electric and magnetic field configurations expressed in terms of field lines on an arbitrary hyperbolic manifold. This electromagnetic field is described by (dual) solutions of…
We give an explicit construction of a positive-definite invariant inner-product for the Klein-Gordon fields, thus solving the old problem of the probability interpretation of Klein-Gordon fields without having to restrict to the subspaces…
We consider a nonlinear Klein--Gordon equation in the nonrelativistic limit regime with initial data in the form of a modulated highly oscillatory exponential. In this regime of a small scaling parameter $\varepsilon$, the solution exhibits…
We show a general method to solve 2+1 dimensional dilatonic Maxwell-Einstein equation with a positive or negative cosmological constant. All the physical solutions are listed with assumptions that they are static, rotationally symmetric,…
We derive the global dynamic properties of the mMKG system (Maxwell coupled with a massive Klein-Gordon scalar field) with a general, unrestrictive class of data, in particular, for Maxwell field of arbitrary size, and by a gauge…
We extend the three-dimensional noncommutative relations of the positions and momenta operators to those in the four dimension. Using the Bopp shift technique, we give the Heisenberg representation of these noncommutative algebras and endow…
We develop a trajectory construction of solutions to the massless wave equation in n+1 dimensions and hence show that the quantum state of a massive relativistic system in 3+1 dimensions may be represented by a stand-alone four-dimensional…
The problem of computing the thermodynamic properties of a one-dimensional gas of particles which transform in the adjoint representation of the gauge group and interact through non-Abelian electric fields is formulated and solved in the…
We prove definitive results on the global stability of the flat space among solutions of the Einstein-Klein-Gordon system. Our main theorems in this monograph include: (1) A proof of global regularity (in wave coordinates) of solutions of…
In this paper, we consider the multi component fields interactions of the complex scalar fields and the electromagnetic fields (Maxwell-Klein-Gordon system) on four dimensional Minkowski spacetime with general gauge couplings and the scalar…
We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong…
I propose a generalization of the Klein-Gordon equation in the framework of AdS space-time and exhibit a four parameter family of solutions among which there is a two parameter family of time-dependent bound states.
We consider a certain ultrahyperbolic equation in a Euclidean space being a generalization of Klein-Gordon-Fock equation. The behavior of solutions at points tending to infinity along timelike directions is studied. We examine the issue of…
We construct two classes of exact solutions to six and higher dimensional Einstein-Maxwell theory in which the metric functions can be written as convolution-like integrals of two special functions. The solutions are regular everywhere and…
We obtain multiplicity results for a class of first-order superquadratic Hamiltonian systems and a class of indefinite superquadratic elliptic systems which lead to the study of strongly indefinite functionals. There is no assumption to the…
In this paper we study solutions of the critical Lane-Emden equation in higher space dimensions. We show that after certain transformations the general solution can be written in terms of elliptic functions. We restrict ourselves to real…