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The Nonlinear Schrödinger Equation

Self-Focusing and Wave Collapse

  • Book
  • © 1999

Overview

Editors:
  1. Catherine Sulem

    1. Department of Mathematics, University of Toronto, Toronto, Canada

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  2. Pirre-Louis Sulem

    1. CNRS UMR 6529, Observatoire de la Côte d’Azur, Nice Cedex 4, France

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Part of the book series: Applied Mathematical Sciences (AMS, volume 139)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Basic Framework

    1. Front Matter

      Pages 1-1
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    2. The Physical Context

      Pages 3-26

    3. Structural Properties

      Pages 27-33

  3. Rigorous Theory

    1. Front Matter

      Pages 41-41
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    2. Existence and Long-Time Behavior

      Pages 43-70

    3. Standing Wave Solutions

      Pages 71-92

    4. Blowup Solutions

      Pages 93-112

  4. Asymptotic Analysis near Collapse

    1. Front Matter

      Pages 113-113
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    2. Numerical Observations

      Pages 115-132

    3. Supercritical Collapse

      Pages 133-140

    4. Critical Collapse

      Pages 141-160

    5. Perturbations of Focusing NLS

      Pages 161-186

  5. Coupling to a Mean Field

    1. Front Matter

      Pages 187-187
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    2. Mean Field Generation

      Pages 189-204

    3. Gravity-Capillary Surface Waves

      Pages 205-220

    4. The Davey-Stewartson System

      Pages 221-242

  6. Coupling to Acoustic Waves

    1. Front Matter

      Pages 243-243
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    2. Langmuir Oscillations

      Pages 245-262

    3. The Scalar Model

      Pages 263-286
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Keywords

Editors and Affiliations

  • Department of Mathematics, University of Toronto, Toronto, Canada

    Catherine Sulem

  • CNRS UMR 6529, Observatoire de la Côte d’Azur, Nice Cedex 4, France

    Pirre-Louis Sulem

Bibliographic Information

  • Book Title: The Nonlinear Schrödinger Equation

  • Book Subtitle: Self-Focusing and Wave Collapse

  • Editors: Catherine Sulem, Pirre-Louis Sulem

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/b98958

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1999

  • Hardcover ISBN: 978-0-387-98611-1Published: 18 June 1999

  • Softcover ISBN: 978-1-4757-7307-1Published: 14 March 2013

  • eBook ISBN: 978-0-387-22768-9Published: 30 June 2007

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: XVI, 350

  • Topics: Analysis, Fluid- and Aerodynamics

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