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Full Description
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
Contents
1. Introduction 2. Darboux Transformation of the Fundamental Nonlinear Schrödinger Equation 3. Darboux Transformation of Higher-Order Nonlinear Schrödinger Equations 4. Darboux Transformation of Coupled Nonlinear Schrödinger Equations 5. Darboux Transformation of Two- and Three-Dimensional Nonlinear Schrödinger Equation 6. Darboux Transformation of a Generalized Nonlinear Schrödinger Equation with Function Coefficients 7. Darboux Transformation of Discrete Nonlinear Schrödinger Equation 8. Darboux Transformation of Nonlocal Nonlinear Schrödinger Equation 9. Lax Pair Search Method 10. Other Integrable Nonlinear Differential Equations Appendix A: Mathematica Codes Appendix B: List of Lax Pairs Presented in this Book Bibliography. Index.
