Nonlinear geometric optics for short pulses

DOI10.1006/jdeq.2001.4016zbMath1006.35015OpenAlexW2046367157MaRDI QIDQ1604509

Jeffrey Rauch, Deborah Alterman

Publication date: 4 July 2002

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2001.4016

zbMATH Keywords

asymptoticsscalingdiffractive geometric opticsnonlinear transport equationtransport of jump discontinuities

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with optics and electromagnetic theory (35Q60) Geometric optics (78A05)

Related Items (10)

INTERMEDIATE MODEL FOR SPATIAL EVOLUTION IN NONLINEAR OPTICS ⋮ Rigorous justification of the short-pulse equation ⋮ Nonlinear geometric optics for reflecting uniformly stable pulses ⋮ Focusing of spherical nonlinear pulses in ${\mathbb R}^{1+3}$ ⋮ Justification of the NLS approximation for a quasilinear water wave model ⋮ Focusing of spherical nonlinear pulses in \(\mathbb R^{1+3}\). II: Nonlinear caustic ⋮ A numerical study of the long-wave short-wave resonance for 3D water waves ⋮ Focusing of spherical nonlinear pulses for nonlinear wave equations ⋮ NONLINEAR ASYMPTOTICS FOR HYPERBOLIC INTERNAL WAVES OF SMALL WIDTH ⋮ A deterministic model for the propagation of turbulent oscillations

Cites Work

• Interaction of nonlinear progressing waves for semilinear wave equations
• The Cauchy problem for semilinear hyperbolic systems with discontinuous data
• Propagation and interaction of singularities in nonlinear hyperbolic problems
• Asymptotic expansions of the solutions to a class of quasilinear hyperbolic initial value problems
• Resonantly Interacting Weakly Nonlinear Hyperbolic Waves. I. A Single Space Variable
• Solutions Containing a Large Parameter of a Quasi-Linear Hyperbolic System of Equations and their Nonlinear Geometric Optics Approximation
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