Applied Mathematical Sciences

Self-Focusing and Wave Collapse

By: Catherine Sulem, Pierre-Louis Sulem

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Hardcover | 18 June 1999

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Hardcover
372 Pages

Dimensions(cm)
24.77 x 17.15 x 1.91

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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.

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Preface
Basic Framework	p. 1
The Physical Context	p. 3
Structural Properties	p. 27
Rigorous Theory	p. 41
Existence and Long-Time Behavior	p. 43
Standing Wave Solutions	p. 71
Blowup Solutions	p. 93
Asymptotic Analysis near Collapse	p. 113
Numerical Observations	p. 115
Supercritical Collapse	p. 133
Critical Collapse	p. 141
Perturbations of Focusing NLS	p. 161
Coupling to a Mean Field	p. 187
Mean Field Generation	p. 189
Gravity-Capillary Surface Waves	p. 205
The Davey-Stewartson System	p. 221
Coupling to Acoustic Waves	p. 243
Langmuir Oscillations	p. 245
The Scalar Model	p. 263
Progressive Waves in Plasmas	p. 287
Synopsis	p. 307
References	p. 309
Name Index	p. 339
Subject Index	p. 347
Table of Contents provided by Blackwell. All Rights Reserved.

Applied Mathematical Sciences

Self-Focusing and Wave Collapse

At a Glance

Hardcover

Shipping

How to return your order

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