WKB asymptotics for the Euler-Maxwell equations

Abstract- The Euler-Maxwell system of equations is a complex, hydrodynamical model for the description of laser-plasma interactions. We introduce non-dimensional variables, exhibit a small parameter ε and study various WKB approximations with re-spect to ε for this system, under a polarization condition for the initial data. We justify an approximation by a weak Zakharov equation for times O(1) and an approximation by a Davey-Stewartson equation for times O( | log ε|). Our key observation is that the Euler-Maxwell exhibit transparency properties, similar to the properties exhibited by Joly, Métivier and Rauch for Maxwell-Bloch systems. These properties imply in particular that in a weakly nonlinear regime, the geometric optics approximation is given by a linear equation.