Coherent nonlinear waves and the Wiener algebra

DOI10.5802/aif.1393zbMath0791.35019OpenAlexW2320100317MaRDI QIDQ1323155

Guy Metivier, Jeffrey Rauch, Jean-Luc Joly

Publication date: 18 July 1994

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1994__44_1_167_0

zbMATH Keywords

oscillatory solutionsconstant coefficientscrystal opticsWiener algebrageometric opticsapplication to conical refractioninteraction of high frequency solutionssemilinear first order symmetric hyperbolic system

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) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Asymptotic expansions of solutions to PDEs (35C20) Initial value problems for first-order hyperbolic systems (35L45)

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Cites Work

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• Asymptotic solutions of oscillatory initial value problems
• The validity of nonlinear geometric optics for weak solutions of conservation laws
• Microlocal structure of involutive conical refraction
• Multidimensional \(\varepsilon\)-stratified waves and oscillations
• Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves
• Fast singular limits of hyperbolic PDEs
• Resonant one dimensional nonlinear geometric optics
• Ondes asymptotiques et approchees pour des systèmes d'équations aux dérivées partielles non linéaires
• Weakly nonlinear high frequency waves
• Resonantly Interacting Weakly Nonlinear Hyperbolic Waves. I. A Single Space Variable
• Homogenization for semilinear hyperbolic systems with oscillatory data
• Resonantly Interacting, Weakly Nonlinear Hyperbolic Waves. II. Several Space Variables
• A Canonical System of lntegrodifferential Equations Arising in Resonant Nonlinear Acoustics
• Conical refraction in crystal optics and hydromagnetics
• Oscillations semi-linéaires multiphasées compatibles en dimension 2 ou 3 d'espace
• Justification of Multidimensional Single Phase Semilinear Geometric Optics
• Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems
• Coherent and focusing multidimensional nonlinear geometric optics
• Über sachgemäße Cauchyprobleme.