The aim of this paper is to study oscillatory solutions of nonlinear hyperbolic systems in the framework developed during the last decade by J.-L. Joly, G. Métivier, and J. Rauch. Here we focus mainly on rectification effects, that is, the interaction of oscillations with a mean field created by the nonlinearity. A real interaction can occur only under some geometric conditions described in [JMR1] and [L1] that are generally not satisfied by the physical models except in the 1-dimensional case. We introduce here a new type of ansatz that allows us to obtain rectification effects under weaker assumptions. We obtain a new class of profile equations and construct solutions for a subclass. Finally, the stability of the asymptotic expansion is proved in the context of Maxwell-Bloch-type systems.
"Long-wave short-wave resonance for nonlinear geometric optics." Duke Math. J. 107 (2) 351 - 419, 1 April 2001. https://doi.org/10.1215/S0012-7094-01-10725-4