This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schroedinger 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 Schroedinger 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, Universite de Cergy-Pontoise and Institut des Hautes Etudes Scientifiques, France

About the Author

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

Reviews

"The Nonlinear Schroedinger 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 Schroedinger (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 informationabout the state-of-the-art in the field." (Dmitry E. Pelinovsky, Mathematical Reviews, April, 2016)

Book Information
ISBN 9783319127477
Author Gadi Fibich
Format Hardback
Page Count 862
Imprint Springer International Publishing AG
Publisher Springer International Publishing AG