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Transparent nonlinear geometric optics and Maxwell-Bloch equations. (English) Zbl 1170.78311

From the text: Many results have been obtained in the past decade about the justification of nonlinear geometric optics expansions. All of them consider general equations and make no assumption on the structure of the nonlinear terms. There are cases where these general theorems do not provide satisfactory results. Typically, this happens when interaction coefficients vanish because of the special structure of the equations. This implies that the transport equations are linear instead of being nonlinear. This phenomenon is called transparency. To reach nonlinear regimes, one idea is to consider waves of larger amplitude or, equivalently, of higher energy. The main goal of this paper is to start an analysis of this problem. We perform it within a class of equations which is interesting for three reasons.

MSC:

78A05 Geometric optics
35Q60 PDEs in connection with optics and electromagnetic theory
78A60 Lasers, masers, optical bistability, nonlinear optics
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