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

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

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...

NONRELATIVISTIC LIMIT OF KLEIN-GORDON-MAXWELL TO SCHRÖDINGER-POISSON By PHILIPPE BECHOUCHE, NORBERT J. MAUSER, and SIGMUND SELBERG

We prove that in the nonrelativistic limit c → ∞, where c is the speed of light, solutions of the Klein-Gordon-Maxwell system on R1+3 converge in the energy space C([0, T]; H1) 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 interp...

Nonrelativistic limit of Klein-Gordon-Maxwell to Schrödinger-Poisson

ar X iv : n lin / 0 50 20 02 v 1 [ nl in . P S ] 1 F eb 2 00 5 Discrete peakons

We demonstrate for the first time the possibility for explicit construction in a discrete Hamiltonian model of an exact solution of the form exp(−|n|), i.e., a discrete peakon. These discrete analogs of the well-known, continuum peakons of the Camassa-Holm equation [Phys. Rev. Lett. 71, 1661 (1993)] are found in a model different from their continuum siblings. Namely, we observe discrete peakon...

On the asymptotic analysis of the Dirac-Maxwell system in the nonrelativistic limit

We deal with the “nonrelativistic limit”, i.e. the limit c → ∞, where c is the speed of light, of the nonlinear PDE system obtained by coupling the Dirac equation for a 4-spinor to the Maxwell equations for the self-consistent field created by the “moving charge” of the spinor. This limit, sometimes also called “Post-Newtonian” limit, yields a SchrödingerPoisson system, where the spin and the m...