Results 61 to 70 of about 1,170 (90)

On some discrete model of the magnetic Laplacian [PDF]

arXiv, 2004
We construct some intrinsically defined discrete model of the magnetic Laplacian. The existence and uniqueness of solutions of the Dirichlet problem for the difference Poisson type equation are proved. We study in detail properties of the discrete model including the limiting process in the two-dimensional Euclidean case.
arxiv  

Well-posedness results for the 3D Zakharov-Kuznetsov equation

, 2011
We prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov equation $\partial_tu+\Delta\partial_xu+ u\partial_xu=0$ in the Sobolev spaces $H^s(\R^3)$, $s>1$, as well as in the Besov space $B^{1,1}_2(\R^3)$.
Ribaud, Francis, Vento, Stéphane
core   +1 more source

Equations of Maxwell Type [PDF]

arXiv, 2009
For an elliptic complex of first order differential operators on a smooth manifold, we define a system of two equations which can be thought of as abstract Maxwell equations. The formal theory of this system proves to be very similar to that of classical Maxwell's equations.
arxiv  

On guided electromagnetic waves in photonic crystal waveguides [PDF]

Amer. Math. Soc. Transl. v. 231, AMS, 2010, pp. 99-108, 2009
The paper addresses the issue of existence and confinement of electromagnetic modes guided by linear defects in photonic crystals. Sufficient condition are provided for existence of such waves near a given spectral location. Confinement to the guide is achieved due to a photonic band gap in the bulk dielectric medium.
arxiv  

Longitudinal dielectric permeability of the quantum degenerate collisional plasmas [PDF]

arXiv, 2010
Dielectric permeability of the degenerate electronic gas for the collisional plasmas is found. The kinetic equation of Wigner -- Vlasov -- Boltzmann with integral of collisions in relaxation form in coordinate space is used. We will notice that dielectric permeability with using of the relaxation equation in the momentum space has been received by ...
arxiv  

Regularity Results for Generalized Electro-Magnetic Problems [PDF]

Analysis (Munich), 30, (2010), 225-252, 2011
We prove regularity results up to the boundary for time independent generalized Maxwell equations on Riemannian manifolds with boundary using the calculus of alternating differential forms. We discuss homogeneous and inhomogeneous boundary data and show 'polynomially weighted' regularity in exterior domains as well.
arxiv  

Standing waves of modified Schrödinger equations coupled with the Chern-Simons gauge theory [PDF]

arXiv, 2017
We are interested in standing waves of a modified Schr\"odinger equation coupled with the Chern-Simons gauge theory. By applying a constraint minimization of Nehari-Pohozaev type, we prove the existence of radial ground state solutions. We also investigate the non-existence for nontrivial solutions.
arxiv  

Nonlinear Schrödinger equation with bounded magnetic field [PDF]

arXiv, 2019
The paper studies existence of solutions for the nonlinear Schr\"odinger equation with a general bounded external magnetic field. In particular, no lattice periodicity of the magnetic field or presence of external electric field is required. Solutions are obtained by means of a general structural statement about bounded sequences in the magnetic ...
arxiv  

Dichotomy Results for the Electromagnetic Schrödinger Equation [PDF]

arXiv
The electromagnetic nonlinear Schr\"odinger (emNLS) equation is a variant of the well-studied nonlinear Schr\"odinger equation. In this article, we consider questions of global existence or blow-up for emNLS in dimensions 3 and higher.
arxiv  

Computation of the fundamental solution of electrodynamics for anisotropic materials

Open Mathematics, 2012
Yakhno Valery, Yaslan Handan, Yakhno Tatiana   +2 more
doaj   +1 more source