Short Pulses Approximations in Dispersive Media

DOI10.1137/070711724zbMath1200.35182arXiv0712.3940OpenAlexW2001113120MaRDI QIDQ3553806

David Lannes, Mathieu Colin

Publication date: 21 April 2010

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.3940

zbMATH Keywords

modified Schrödinger equationslowly varying envelopechirped pulsesfastly oscillating initial dataSchrödinger approximation

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) Initial value problems for first-order hyperbolic systems (35L45) Geometric optics (78A05)

Related Items

INTERMEDIATE MODEL FOR SPATIAL EVOLUTION IN NONLINEAR OPTICS ⋮ On a Lagrangian reduction and a deformation of completely integrable systems ⋮ Rigorous justification of the short-pulse equation ⋮ Approximation of High-Frequency Wave Propagation in Dispersive Media ⋮ Dynamics of the black soliton in a regularized nonlinear Schrödinger equation ⋮ Unnamed Item ⋮ Nonlinear geometric optics method-based multi-scale numerical schemes for a class of highly oscillatory transport equations ⋮ Norm-inflation with Infinite Loss of Regularity for Periodic NLS Equations in Negative Sobolev Spaces ⋮ Geometric optics and instability for NLS and Davey-Stewartson models ⋮ On the Cauchy problem for the Hartree type equation in the Wiener algebra ⋮ Global Well-Posedness of the Short-Pulse and Sine–Gordon Equations in Energy Space ⋮ On the Cauchy problem for Wigner-Poisson-BGK equation in the Wiener algebra ⋮ Boundedness of planar jump discontinuities for homogeneous hyperbolic systems

This page was built for publication: Short Pulses Approximations in Dispersive Media