Finite energy standing waves for the Klein-Gordon-Maxwell system: the limit case

Non-relativistic limit of Klein-Gordon Maxwell

We deal with the derivation of the Schrödinger-Poisson system as a non-relativistic limit (i.e. c→∞ where c is the speed of light) of the Klein-GordonMaxwell or the Dirac-Maxwell system on R. We deal with convergence in the energy space C([0, T ];H). We use and motivate a splitting of the scalar Klein-Gordon field into a sum of two fields, corresponding, in the physical interpretation, to elect...

Strong instability of standing waves for nonlinear Klein-Gordon equation and Klein-Gordon-Zakharov system

The orbital instability of ground state standing waves eφω(x) for the nonlinear Klein-Gordon equation has been known in the domain of all frequencies ω for the supercritical case and for frequencies strictly less than a critical frequency ωc in the subcritical case. We prove the strong instability of ground state standing waves for the entire domain above. For the case when the frequency is equ...

Orbital Stability for Periodic Standing Waves of the Klein-gordon-zakharov System and the Beam Equation

The existence and stability of spatially periodic waves (eφω, ψω) in the KleinGordon-Zakharov (KGZ) system are studied. We show a local existence result for low regularity initial data. Then, we construct a one-parameter family of periodic dnoidal waves for (KGZ) system when the period is bigger than √ 2π. We show that these waves are stable whenever an appropriate function satisfies the standa...

Strong Instability of Standing Waves for Nonlinear Klein-gordon Equations

The strong instability of ground state standing wave solutions eφω(x) for nonlinear Klein-Gordon equations has been known only for the case ω = 0. In this paper we prove the strong instability for small frequency ω.

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