Justification of a nonlinear Schrödinger model for laser beams in photopolymers

DOI10.1007/S00033-013-0338-9zbMath1296.35175OpenAlexW2088387875MaRDI QIDQ743537

D. Kharzeev

Publication date: 25 September 2014

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-013-0338-9

zbMATH Keywords

nonlinear Schrödinger equationlocal well-posednessa priori energy estimatesjustification of amplitude equations

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) NLS equations (nonlinear Schrödinger equations) (35Q55) Maxwell equations (35Q61) Initial value problems for second-order hyperbolic systems (35L52)

Related Items (3)

Validity of the Weakly Nonlinear Solution of the Cauchy Problem for the Boussinesq-Type Equation ⋮ NLS ground states on the half-line with point interactions ⋮ Prescribed mass ground states for a doubly nonlinear Schrödinger equation in dimension one

Cites Work

• Unnamed Item
• Unnamed Item
• Rigorous justification of the short-pulse equation
• Diffractive optics with harmonic radiation in 2d nonlinear photonic crystal waveguide
• Compressible fluid flow and systems of conservation laws in several space variables
• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Existence and stability of modulating pulse solutions in Maxwell's equations describing nonlinear optics
• Transparent nonlinear geometric optics and Maxwell-Bloch equations.
• Global solutions to Maxwell equations in a ferromagnetic medium
• Partial differential equations. 3: Nonlinear equations
• Global solvability of the Maxwell-Bloch equations from nonlinear optics
• ASYMPTOTIC DECAY OF A ONE-DIMENSIONAL WAVE PACKET IN A NONLINEAR DISPERSIVE MEDIUM
• The validity of modulation equations for extended systems with cubic nonlinearities
• Diffractive nonlinear geometric optics with rectification
• Dispersive nonlinear geometric optics
• Catching light in its own trap

This page was built for publication: Justification of a nonlinear Schrödinger model for laser beams in photopolymers