The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse: Self-Focusing and Wave Collapse

✍ Scribed by Catherine Sulem, Pirre-Louis Sulem (eds.)

• Publisher: Springer-Verlag New York
• Year: 1999
• Tongue: English
• Leaves: 338
• Series: Applied Mathematical Sciences 139
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvi
Front Matter....Pages 1-1
The Physical Context....Pages 3-26
Structural Properties....Pages 27-33
Front Matter....Pages 41-41
Existence and Long-Time Behavior....Pages 43-70
Standing Wave Solutions....Pages 71-92
Blowup Solutions....Pages 93-112
Front Matter....Pages 113-113
Numerical Observations....Pages 115-132
Supercritical Collapse....Pages 133-140
Critical Collapse....Pages 141-160
Perturbations of Focusing NLS....Pages 161-186
Front Matter....Pages 187-187
Mean Field Generation....Pages 189-204
Gravity-Capillary Surface Waves....Pages 205-220
The Davey-Stewartson System....Pages 221-242
Front Matter....Pages 243-243
Langmuir Oscillations....Pages 245-262
The Scalar Model....Pages 263-286
Progressive Waves in Plasmas....Pages 287-305
Back Matter....Pages 307-352

✦ Subjects

Analysis;Fluids