Darboux Transformation of Nonlinear Schrödinger Equations: A Guide and a Tutorial

By Laila Al Sakkaf and Usama Al Khawaja

Darboux Transformation of Nonlinear Schr dinger Equations: A Guide and a Tutorial is an easy to follow guide for the application of the Darboux transformation (DT) to the nonlinear Schr dinger equation (NLSE), including all versions that admit a Lax Pair such as integrable NLSEs. It comes packed with detailed calculations leading to exact solutions, worked examples, and downloadable Mathematica code. Often these materials are scattered across various papers and different textbooks, or they focus on various nonlinear differential equations. The present book will be totally focused on NLSE, which allows for extensive details to be presented. It is suitable for graduate researchers conducting specialized research in nonlinear physics and applied mathematics.

Key Features:

- Contains a large number of worked-out examples in detail.

- Provides tips, shortcuts, and subtle details in obtaining exact solutions.

- Presents a systematic search method for finding Lax Pairs.

- Compiles a list of all known Lax Pairs to the NLSEs considered in the book.

- Applies the method to other nonlinear equations, including the KdV and AKNS systems.

• Format: Hardcover
• Language: English
• ISBN: 1041018258
• ISBN13: 9781041018254
• Release Date: July 2026
• Publisher: CRC Press
• Length: 272 Pages