Recent results in large amplitude monophase nonlinear geometric optics

International audienceMany works are devoted to the study of high frequency oscillatory nonlinear waves. For quasilinear first order systems, the standard regime is weakly nonlinear geometric optics which consider near some background state perturbations of amplitude $ \eps $ with wave length $ \eps $ (and $ \eps \in ]0,1] $ is going to $ 0 $). However, when the oscillations can be associated to a linearly degenerate mode, as it is the case for incompressible Euler equations, stronger waves can also be considered. The question of the existence, the propagation and the interaction of such larger amplitude waves is the matter of supercritical BKW analysis. What follows describes recent results in this direction