Long-wave short-wave resonance for nonlinear geometric optics.
type: Item
instance of: scholarly article
title: Long-wave short-wave resonance for nonlinear geometric optics.
zbMATH Open document ID: 1034.35133
DOI: 10.1215/S0012-7094-01-10725-4
author: Thierry Colin
author: David Lannes
published in: Duke Mathematical Journal
publication date: 2002-10-27T00:00:00Z
review text: This paper studies oscillatory solutions of nonlinear hyperbolic systems, with attention focussed mainly on the interaction of oscillations with a mean field created by the nonlinearity (rectification effects). A new class of profile equations is obtained and used to construct solutions for a sub-class. Finally, the stability of the asymptotic expansion is proved in connection with Maxwell-Bloch-type systems.
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 78A60
Mathematics Subject Classification ID: 35B34
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35L60
zbMATH DE Number: 1820804
zbMATH Keywords: oscillatory solutions
zbMATH Keywords: Maxwell-Bloch-type systems
reviewed by: Alan Jeffrey
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1820804