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The Nonlinear Schroedinger Equation : Self-Focusing and Wave Collapse - Catherine Sulem

The Nonlinear Schroedinger Equation

Self-Focusing and Wave Collapse

Hardcover

Published: 18th June 1999
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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 rigorous mathematical analysis to formal asymptotic expansions and numerical simulations.

Preface
Basic Frameworkp. 1
The Physical Contextp. 3
Structural Propertiesp. 27
Rigorous Theoryp. 41
Existence and Long-Time Behaviorp. 43
Standing Wave Solutionsp. 71
Blowup Solutionsp. 93
Asymptotic Analysis near Collapsep. 113
Numerical Observationsp. 115
Supercritical Collapsep. 133
Critical Collapsep. 141
Perturbations of Focusing NLSp. 161
Coupling to a Mean Fieldp. 187
Mean Field Generationp. 189
Gravity-Capillary Surface Wavesp. 205
The Davey-Stewartson Systemp. 221
Coupling to Acoustic Wavesp. 243
Langmuir Oscillationsp. 245
The Scalar Modelp. 263
Progressive Waves in Plasmasp. 287
Synopsisp. 307
Referencesp. 309
Name Indexp. 339
Subject Indexp. 347
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387986111
ISBN-10: 0387986111
Series: Applied Mathematical Sciences
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 350
Published: 18th June 1999
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 1.54