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Handbook of Exact Solutions to the Nonlinear Schrödinger Equations

Usama Al Khawaja, Laila Al Sakkaf


This book is the result of years of work by the authors, looking to serve the research communities involved with the NLSE by collecting all known solutions in one resource. In addition, the book organizes the solutions by classifying and grouping them based on aspects and symmetries they possess. Although most of the solutions presented in this book have been derived elsewhere using various methods, the authors present a systematic derivation of many solutions and even include new derivations. They have also presented symmetries and reductions that connect different solutions through transformations and enable classifying new solutions into known classes. 

For the user to verify that the presented solutions do satisfy the NLSE, this monumental work is accompanied by Mathematica notebooks containing all solutions. This work also features a large number of figures, and animations are included to help visualize solutions and their dynamics.

About Editors

Usama Al Khawaja obtained his bachelor's and master's degrees in physics from The University of Jordan in 1992 and 1996 respectively. He earned his PhD degree in theoretical physics from the University of Copenhagen in 1999. He spent three years of postdoctoral research at Utrecht University in the Netherlands before joining the United Arab Emirates University in 2002 as an assistant professor. He is currently a full professor and Chairman of the physics department at the United Arab Emirates University. His main areas of research are Bose–Einstein condensation, nonlinear and quantum optics, integrability and exact solutions. He has authored more than 70 papers and obtained one patent on applying discrete solitons in all-optical operations.

Laila Al Sakkaf obtained her bachelor's and then her master's degree in physics from the United Arab Emirates University in 2015 and 2018. She is currently a research assistant and a PhD student at the physics department of the United Arab Emirates University. Her current research focus is on integrability and exact solutions of differential equations modeling nonlinear physical phenomena.

Table of Contents



Author biography


1 Introduction

2 Fundamental Nonlinear Schrödinger Equation

3 Nonlinear Schrödinger Equation with Power Law and Dual Power Law Nonlinearities

4 Nonlinear Schrödinger Equation with Higher Order Terms

5 Scaling Transformations

6 Nonlinear Schrödinger Equation in (N+1)-Dimensions

7 Coupled Nonlinear Schrödinger Equations

8 Discrete Nonlinear Schrödinger Equations

9 Non-Local Nonlinear Schrödinger Equations

A Derivation of Some Solutions of Chapters 2 and 3

B Darboux Transformation

C Derivation of the Similarity Transformations in Chapter 5


Hardback ISBN: 9780750324267

Ebook ISBN: 9780750324281

DOI: 10.1088/2053-2563/ab2f31

Publisher: Institute of Physics Publishing


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