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 respect 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.