Long-wave short-wave resonance for nonlinear geometric optics.

DOI10.1215/S0012-7094-01-10725-4zbMath1034.35133MaRDI QIDQ1847823

David Lannes, Thierry Colin

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

oscillatory solutionsMaxwell-Bloch-type systems

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with optics and electromagnetic theory (35Q60) First-order nonlinear hyperbolic equations (35L60) Asymptotic expansions of solutions to PDEs (35C20) Lasers, masers, optical bistability, nonlinear optics (78A60) Resonance in context of PDEs (35B34)

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Cites Work

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• Local solution for the Kadomtsev-Petviashvili equation in \(\mathbb{R}^ 2\)
• Diffractive nonlinear geometric optics with rectification
• On a nonlinear Schrödinger equation arising in the theory of water waves

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