Handbook of Exact Solutions to the Nonlinear Schrödinger Equations (Second Edition) (eBook, ePUB)
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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.This book is the result of years of work by the author...
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.
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 the aspects and symmetries they possess. 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.
This expanded second edition contains new solutions published or derived since the first edition. 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.
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 the aspects and symmetries they possess. 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.
This expanded second edition contains new solutions published or derived since the first edition. 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.
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