The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse
Author:   Catherine Sulem ,  Pierre-Louis Sulem
Publisher:   Springer-Verlag New York Inc.
Edition:   1999 ed.
Volume:   139
ISBN:  

9780387986111


Pages:   350
Publication Date:   18 June 1999
Format:   Hardback
Availability:   In Print   Availability explained
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The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse


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Overview

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.

Full Product Details

Author:   Catherine Sulem ,  Pierre-Louis Sulem
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1999 ed.
Volume:   139
Dimensions:   Width: 15.50cm , Height: 2.20cm , Length: 23.50cm
Weight:   1.540kg
ISBN:  

9780387986111


ISBN 10:   0387986111
Pages:   350
Publication Date:   18 June 1999
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

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.

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