Validity of nonlinear geometric optics with times growing logarithmically

DOI10.1090/S0002-9939-00-05845-7zbMath0980.35093OpenAlexW1582854041MaRDI QIDQ2701585

Jeffrey Rauch, David Lannes

Publication date: 19 February 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-00-05845-7

zbMATH Keywords

large time asymptoticsnonlinear geometric opticscorrector

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with optics and electromagnetic theory (35Q60) Singular perturbations in context of PDEs (35B25) First-order nonlinear hyperbolic equations (35L60) Asymptotic expansions of solutions to PDEs (35C20) Lasers, masers, optical bistability, nonlinear optics (78A60)

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Cites Work

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• Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves
• Solutions analytic in time are not dense
• Fast singular limits of hyperbolic PDEs
• Resonant one dimensional nonlinear geometric optics
• A Canonical System of lntegrodifferential Equations Arising in Resonant Nonlinear Acoustics
• Diffractive nonlinear geometric optics with rectification
• Global Oscillatory Waves for Second Order Quasilinear Wave Equations
• Diffractive Nonlinear Geometric Optics for Short Pulses
• Coherent and focusing multidimensional nonlinear geometric optics

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