WAVE TRANSMISSION IN DISPERSIVE MEDIA

DOI10.1142/S0218202507002005zbMath1220.35170OpenAlexW2023281579MaRDI QIDQ5297204

Vincent Lescarret

Publication date: 18 July 2007

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202507002005

zbMATH Keywords

hyperbolicgeometric opticsdispersiveinfinite order correctorsmixted problem

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) PDEs in connection with optics and electromagnetic theory (35Q60)

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INTERMEDIATE MODEL FOR SPATIAL EVOLUTION IN NONLINEAR OPTICS ⋮ Weakly nonlinear surface waves on the plasma-vacuum interface ⋮ Weakly Nonlinear Multiphase Geometric Optics for Hyperbolic Quasilinear Boundary Value Problems: Construction of a Leading Profile ⋮ Weak well-posedness of hyperbolic boundary value problems in a strip: when instabilities do not reflect the geometry ⋮ Transverse instability of high frequency weakly stable quasilinear boundary value problems ⋮ Geometric optics expansions with amplification for hyperbolic boundary value problems: linear problems ⋮ Geometric Optics for Surface Waves in Nonlinear Elasticity ⋮ Geometric Optics Expansions for Hyperbolic Corner Problems II: From Weak Stability to Violent Instability ⋮ WKB EXPANSIONS FOR HYPERBOLIC BOUNDARY VALUE PROBLEMS IN A STRIP: SELFINTERACTION MEETS STRONG WELL-POSEDNESS ⋮ Nonlinear geometric optics for reflecting uniformly stable pulses ⋮ Weakly nonlinear surface waves in magnetohydrodynamics. I ⋮ Diffractive wave transmission in dispersive media ⋮ Amplification of pulses in nonlinear geometric optics ⋮ Resonant Leading Order Geometric Optics Expansions for Quasilinear Hyperbolic Fixed and Free Boundary Problems ⋮ Resonant Leading Term Geometric Optics Expansions with Boundary Layers for Quasilinear Hyperbolic Boundary Problems ⋮ WKB expansions for weakly well-posed hyperbolic boundary value problems in a strip: Time depending loss of derivatives

Cites Work

• Multidimensional \(\varepsilon\)-stratified waves and oscillations
• Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves
• Secular growth estimates for hyperbolic systems.
• Probleme Mixte Hyperbolique Quasi-Lineaire Caracteristique
• Dispersive nonlinear geometric optics
• A General Framework for Diffractive Optics and Its Applications to Lasers with Large Spectrums and Short Pulses
• Coherent and focusing multidimensional nonlinear geometric optics
• The modulation equations of nonlinear geometric optics
• Boundary value problems for first order operators

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