Semi-classical analysis for nonlinear Schrödinger equations /

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These lecture notes review recent results on the high-frequency analysis of nonlinear Schrödinger equations in the presence of an external potential. The book consists of two relatively independent parts: WKB analysis, and caustic crossing. In the first part, the basic linear WKB theory is construc...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Carles, Rémi
Format: Electronic eBook
Language:Inglés
Published: Singapore ; Hackensack, NJ : World Scientific, ©2008.
Subjects:
Schrödinger equation.
Nonlinear theories.
Équation de Schrödinger.
Théories non linéaires.
SCIENCE > Waves & Wave Mechanics.
Nonlinear theories
Schrödinger equation
Online Access:Texto completo
Table of Contents:
  • WKB analysis
  • Weak nonlinear geometric optics
  • Convergence of quadratic observables via modulated energy functionals
  • Pointwise description of the wave function
  • Some instability phenomena
  • Caustic crossing : the case of focal points
  • Caustic crossing : formal analysis
  • Focal point without external potential
  • Focal point in the presence of an external potential
  • Some ideas for supercritical cases.

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