(Ebook) Handbook of Exact Solutions to the Nonlinear Schrödinger Equations by Usama Al Khawaja, Laila Al Sakkaf ISBN 9780750324267, 9780750324281, 0750324260, 0750324287

(Ebook) Handbook of Exact Solutions to the Nonlinear Schrödinger Equations by Usama Al Khawaja, Laila Al Sakkaf ISBN 9780750324267, 9780750324281, 0750324260, 0750324287

Main subject categories: • Nonlinear Schrödinger Equation • Nonlinear Schrödinger Equation with Power Law and Dual Power Law Nonlinearities • Nonlinear Schrödinger Equation with Higher Order Terms • Scaling Transformations • Nonlinear Schrödinger Equation in (N + 1)-Dimensions • Coupled Nonlinear Schrödinger Equations • Discrete Nonlinear Schrödinger Equation • Nonlocal Nonlinear Schrödinger Equation • Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) • Schrödinger operator, Schrödinger equation • Partial differential equations of mathematical physics and other areas of application

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.

For the user to verify that the presented solutions do satisfy the NLSE, this monumental work is accompanied by Mathematica notebooks containing all solutions. This work also features a large number of figures, and animations are included to help visualize solutions and their dynamics.