Darboux Transformation of Nonlinear Schrödinger Equations: a Guide and Tutorial

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. 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