ar X iv : m at h / 02 02 20 1 v 1 [ m at h . A P ] 2 0 Fe b 20 02 Nonrelativistic limit of Klein - Gordon - Maxwell to Schrödinger - Poisson

m at h . A P / 02 02 20 1 v 1 20 F eb 2 00 2 Nonrelativistic limit of Klein - Gordon - Maxwell to Schrödinger - Poisson Philippe

We prove that in the nonrelativistic limit c → ∞, where c is the speed of light, solutions of the Klein-Gordon-Maxwell system on R 1+3 converge in the energy space C([0, T ]; H 1) to solutions of a Schrödinger-Poisson system, under appropriate conditions on the initial data. This requires the splitting of the scalar Klein-Gordon field into a sum of two fields, corresponding, in the physical int...

ar X iv : m at h / 03 02 33 9 v 1 [ m at h . A P ] 2 7 Fe b 20 03 NONLINEAR SCHRÖDINGER EQUATIONS WITH STARK POTENTIAL

We study the nonlinear Schrödinger equations with a linear potential. A change of variables makes it possible to deduce results concerning finite time blow up and scattering theory from the case with no potential.

ar X iv : a st ro - p h / 04 02 02 0 v 1 1 Fe b 20 04 Perspective from a Younger Generation – The Astro - Spectroscopy of Gisbert

ar X iv : m at h / 02 02 11 4 v 1 [ m at h . G N ] 1 2 Fe b 20 02 ON FINITE - DIMENSIONAL MAPS II

Let f : X → Y be a perfect n-dimensional surjective map of paracompact spaces and Y a C-space. We consider the following property of continuous maps g : X → Ik = [0, 1], where 1 ≤ k ≤ ω: each g(f(y)), y ∈ Y , is at most n-dimensional. It is shown that all maps g ∈ C(X, In+1) with the above property form a dense Gδ-set in the function space C(X, I n+1 ) equipped with the source limitation topolo...

ar X iv : m at h / 06 02 37 1 v 1 [ m at h . A G ] 1 7 Fe b 20 06 Braid Monodromy of Hypersurface Singularities