Publisher's Synopsis
Throughout the long history of the nonlinear Schrödinger equation (NLSE), many exact analytical solutions have been found and they continue to grow as new solutions are being sought and discovered. As the basis for theoretical models in various research fields as diverse as Bose-Einstein condensates of ultracold gases, condensed matter, nonlinear optics and deep water waves, this equation is the subject of interest in numerous scientific communities. Accordingly, its known solutions are scattered in the literatures of the different fields. For a beginner, as well as for an expert researcher, it is difficult to keep track of the large number of known solutions. It is important for a researcher or a reviewer to know if a certain solution is a new solution, belongs to an existing class of solutions, or can be trivially obtained from another solution by a transformation.
This book is the result of years of work by the authors, looking to serve the research communities involved with the NLSE by collecting all known solutions in one resource. In addition, the book organizes the solutions by classifying and grouping them based on aspects and symmetries they possess. Although most of the solutions presented in this book have been derived elsewhere using various methods, the authors present a systematic derivation of many solutions and even include new derivations. They have also presented symmetries and reductions that connect different solutions through transformations and enable classifying new solutions into known classes.
This expanded second edition contains new solutions published or derived since the first edition and noting the increasing interest in and applications of the fractional nonlinear Schrödinger equation, a new chapter devoted to this topic has been added. Each chapter now also features an introductory section documenting the history, background, and physical systems described by the equations at hand.
Key Features:
- Comprehensive and fully up to date. Detailed consideration of the main NLSE models.
- Includes animated figures to help visualize solutions and their dynamics.
- Accompanying Mathematica code including dynamics of solutions.
- New chapter on Fractional Nonlinear Schrödinger Equation
