Transparent Nonlinear Geometric Optics and Maxwell–Bloch Equations

✍ Scribed by Jean-Luc Joly; Guy Metivier; Jeffrey Rauch

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 443 KB
• Volume: 166
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.2000.3794

✦ Synopsis

Many results have been obtained in the past decade about the justification of nonlinear geometric optics expansions (see references below and the survey papers [JMR1, JMR2]). 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 in [Do]. 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. First, it contains several versions of Maxwell Bloch equations which are of special interest in nonlinear optics. Second, it is sufficiently general to capture most of the