Darboux Transformation of Nonlinear Schrödinger Equations
eBook - ePub

Darboux Transformation of Nonlinear Schrödinger Equations

A Guide and a Tutorial

  1. 250 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Darboux Transformation of Nonlinear Schrödinger Equations

A Guide and a Tutorial

About this book

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

Information

Publisher
CRC Press
Year
2026
Print ISBN
9781041018254
eBook ISBN
9781040615256
Edition
1
Topic
Physical Sciences
Subtopic
Mathematical & Computational Physics

Table of contents

  1. Cover Page
  2. Half-Title Page
  3. Title Page
  4. Copyright Page
  5. Dedication Page
  6. Contents
  7. Preface
  8. Author Biographies
  9. Acknowledgments
  10. 1 Introduction
  11. 2 Darboux Transformation of the Fundamental Nonlinear Schrödinger Equation
  12. 3 Darboux Transformation of Higher-Order Nonlinear Schrödinger Equations
  13. 4 Darboux Transformation of Coupled Nonlinear Schrödinger Equations
  14. 5 Darboux Transformation of Two- and Three-Dimensional Nonlinear Schrödinger Equation
  15. 6 Darboux Transformation of a Generalized Nonlinear Schrödinger Equation with Function Coefficients
  16. 7 Darboux Transformation of Discrete Nonlinear Schrödinger Equation
  17. 8 Darboux Transformation of Nonlocal Nonlinear Schrödinger Equation
  18. 9 Lax Pair Search Method
  19. 10 Other Integrable Nonlinear Differential Equations
  20. A Mathematica Codes
  21. B List of Lax Pairs Presented in This Book
  22. Bibliography
  23. Index

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