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The Nonlinear Schrödinger Equation

Singular Solutions and Optical Collapse

  • Gadi Fibich

Part of the Applied Mathematical Sciences book series (AMS, volume 192)

Table of contents

  1. Front Matter
    Pages i-xxxi
  2. NLS in Nonlinear Optics I

    1. Front Matter
      Pages 1-1
    2. Gadi Fibich
      Pages 3-18
    3. Gadi Fibich
      Pages 19-60
    4. Gadi Fibich
      Pages 61-88
    5. Gadi Fibich
      Pages 89-92
  3. Rigorous Analysis

    1. Front Matter
      Pages 93-93
    2. Gadi Fibich
      Pages 95-124
    3. Gadi Fibich
      Pages 125-145
    4. Gadi Fibich
      Pages 147-174
    5. Gadi Fibich
      Pages 175-191
    6. Gadi Fibich
      Pages 193-204
    7. Gadi Fibich
      Pages 333-383
    8. Gadi Fibich
      Pages 385-417
  4. Asymptotic Analysis of the Critical NLS

    1. Front Matter
      Pages 419-419
    2. Gadi Fibich
      Pages 421-448
    3. Gadi Fibich
      Pages 449-471
  5. Asymptotic Analysis of the Supercritical NLS

  6. NLS in Nonlinear Optics II

    1. Front Matter
      Pages 551-551
    2. Gadi Fibich
      Pages 571-588
    3. Gadi Fibich
      Pages 589-611
    4. Gadi Fibich
      Pages 613-634
  7. Numerical Methods

    1. Front Matter
      Pages 635-635
    2. Gadi Fibich
      Pages 637-646
    3. Gadi Fibich
      Pages 647-654
    4. Gadi Fibich
      Pages 655-665
  8. The Perturbed Critical NLS

    1. Front Matter
      Pages 667-667
    2. Gadi Fibich
      Pages 669-700
    3. Gadi Fibich
      Pages 701-709
    4. Gadi Fibich
      Pages 711-721
    5. Gadi Fibich
      Pages 743-754
    6. Gadi Fibich
      Pages 755-781
    7. Gadi Fibich
      Pages 793-832
    8. Gadi Fibich
      Pages 833-841
  9. Back Matter
    Pages 843-862

About this book

Introduction

This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results.

The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics.

Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University.

“This book provides a clear presentation of the nonlinear Schrodinger equation and its applications from various perspectives (rigorous analysis, informal analysis, and physics). It will be extremely useful for students and researchers who enter this field.”

Frank Merle, Université de Cergy-Pontoise and Institut des Hautes Études Scientifiques, France

Keywords

Blowup Collapse Dispersive Equations Nonlinear Optics Nonlinear Partial Differential Equations Nonlinear Schrodinger Equation Nonlinear Waves Optical Collapse Self Focusing Singularity

Authors and affiliations

  • Gadi Fibich
    • 1
  1. 1.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-12748-4
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-12747-7
  • Online ISBN 978-3-319-12748-4
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • Buy this book on publisher's site