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© 2015

The Nonlinear Schrödinger Equation

Singular Solutions and Optical Collapse

Textbook

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

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

  1. 1.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

About the authors

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

Bibliographic information

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Reviews

“The Nonlinear Schrödinger Equation (NLS) theory was an object of great interest during last decades. … the present book includes almost all questions connected with theoretical and experimental investigations of the above mentioned matter during the years since 1960 until now. … the book abounds in recent results, facts and examples that makes it very interesting for the researchers who work actively in this field.” (Dimitar A. Kolev, zbMATH, 1351.35001, 2017)

“This monograph is devoted to the analysis of optical collapse modelled by the nonlinear Schrödinger (NLS) equation. … The book contains everything a modern reader wants to learn about the NLS equation. … The book is a nice addition to the existing literature on the subject of the NLS equation. New and experienced researchers alike may use this text to get the latest information about the state-of-the-art in the field.” (Dmitry E. Pelinovsky, Mathematical Reviews, April, 2016)