The Nonlinear Schrödinger Equation - Sulem, Catherine; Sulem, Pierre-Louis
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This monograph aims to fill the gap between the mathematical literature which significantly contributed during the last decade to the understanding of the collapse phenomenon, and applications to domains like plasma physics and nonlinear optics where this process provides a fundamental mechanism for small scale formation and wave dissipation. This results in a localized heating of the medium and in the case of propagation in a dielectric to possible degradation of the material. For this purpose, the authors have chosen to address the problem of wave collapse by several methods ranging from…mehr

Produktbeschreibung
This monograph aims to fill the gap between the mathematical literature which significantly contributed during the last decade to the understanding of the collapse phenomenon, and applications to domains like plasma physics and nonlinear optics where this process provides a fundamental mechanism for small scale formation and wave dissipation. This results in a localized heating of the medium and in the case of propagation in a dielectric to possible degradation of the material. For this purpose, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal asymptotic expansions and numerical simulations.
  • Produktdetails
  • Applied Mathematical Sciences
  • Verlag: Springer, Berlin
  • Erscheinungstermin: Oktober 1999
  • Englisch
  • Abmessung: 241mm x 161mm x 22mm
  • Gewicht: 656g
  • ISBN-13: 9780387986111
  • ISBN-10: 0387986111
  • Artikelnr.: 09239020
Inhaltsangabe
I Basic framework.- II Rigorous theory.- III Asymptotic analysis near collapse.- IV Coupling to a slaved mean field.- V Coupling to acoustic waves.

Basic Framework.- The Physical Context.- Structural Properties.- Rigorous Theory.- Existence and Long-Time Behavior.- Standing Wave Solutions.- Blowup Solutions.- Asymptotic Analysis near Collapse.- Numerical Observations.- Supercritical Collapse.- Critical Collapse.- Perturbations of Focusing NLS.- Coupling to a Mean Field.- Mean Field Generation.- Gravity-Capillary Surface Waves.- The Davey-Stewartson System.- Coupling to Acoustic Waves.- Langmuir Oscillations.- The Scalar Model.- Progressive Waves in Plasmas.