Darboux Transformation of Nonlinear Schrödinger Equations
14 days return policy
Shipping & Delivery
Product details
- ISBN 9781041018254
- Dimensions: 156 x 234mm
- Publication Date: 15 Jul 2026
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Hardback
Secure
checkout
Fast Shipping
Easy returns
Darboux Transformation of Nonlinear Schrödinger Equations: A Guide and a Tutorial is an easy to follow guide for the application of the Darboux transformation (DT) to the nonlinear Schrödinger 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.
Laila Al Sakkaf is an Assistant Professor in the Department of Applied Sciences, College of Engineering, at Abu Dhabi University. Her research interests encompass integrability and exact solutions of differential equations, particularly those modeling nonlinear physical phenomena, including soliton scattering. She developed a highly efficient numerical code based on power expansion for solving nonlinear differential equations. In 2023, Laila obtained a patent on focusing light using acoustic field.
Usama Al Khawaja is a Professor of Physics at the University of Jordan. His main research interests are integrability and exact solutions, nonlinear and quantum optics, quantum computation, and Bose-Einstein condensation. His main achievements in integrability and exact solutions include developing a systematic search method of finding Lax pairs of a given nonlinear partial differential equation. He also developed a highly-accurate convergent power series method for solving regular and fractional nonlinear partial differential equations. He authored more than 100 papers and obtained two patents on applying discrete solitons in all-optical operations, and in converging light using acoustic waves.
