Quasilinear Schr\"odinger systems for laser-plasma interaction

Abstract: In this talk, i will derive from Euler-Maxwell system a new
quasilinear system of Schr\"odinger type in order to compute
laser-plasma interaction. This system describes the interaction of
four types of waves: the laser, the backscattered Raman component, the
plasma-electronic waves and the acoustic waves. From the technical
point of view, it is a dispersive perturbation of a first order non
hyperbolic quasilinear system. Using an adapted symmetrization
process, i will show that it is well posed. I will also provide some
numerical simulation showing the Raman instability.  I will finish by
explaining how one can take into account some diffusion processes like
the Landau effect by coupling PDE's in physical and Fourrier space.