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Applied Mathematical Sciences

The Nonlinear Schrödinger Equation

Singular Solutions and Optical Collapse

Authors: Fibich, Gadi

  • Provides a unique interdisciplinary treatment of the nonlinear Schrödinger equation, combining rigorous analysis, informal analysis, numerical methods and physics
  • Presents all the necessary physical background, and assumes only that the reader has taken an introductory class in partial differential equations
  • Carefully explains the theory, application and background of the nonlinear Schrödinger equation in nonlinear optics
  • Covers the theory of NLS collapse from the early 1960s and up to the present
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eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-12748-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-3-319-12747-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 18, 2016
  • ISBN 978-3-319-37596-0
  • Free shipping for individuals worldwide
About this Textbook

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

About the authors

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

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)


Table of contents (39 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-12748-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-3-319-12747-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 18, 2016
  • ISBN 978-3-319-37596-0
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
The Nonlinear Schrödinger Equation
Book Subtitle
Singular Solutions and Optical Collapse
Authors
Series Title
Applied Mathematical Sciences
Series Volume
192
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-12748-4
DOI
10.1007/978-3-319-12748-4
Hardcover ISBN
978-3-319-12747-7
Softcover ISBN
978-3-319-37596-0
Series ISSN
0066-5452
Edition Number
1
Number of Pages
XXXI, 862
Number of Illustrations and Tables
102 b/w illustrations, 100 illustrations in colour
Topics