Discrete and Continuous Nonlinear Schrodinger Systems

Discrete and Continuous Nonlinear Schrodinger Systems

by M. J. Ablowitz, B. Prinari, A. D. Trubatch
     
 

ISBN-10: 0521534372

ISBN-13: 9780521534376

Pub. Date: 04/28/2013

Publisher: Cambridge University Press

Over the past thirty years significant progress has been made in the investigation of nonlinear waves—including "soliton equations", a class of nonlinear wave equations that arise frequently in such areas as nonlinear optics, fluid dynamics, and statistical physics. The broad interest in this field can be traced to understanding "solitons" and the associated

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Overview

Over the past thirty years significant progress has been made in the investigation of nonlinear waves—including "soliton equations", a class of nonlinear wave equations that arise frequently in such areas as nonlinear optics, fluid dynamics, and statistical physics. The broad interest in this field can be traced to understanding "solitons" and the associated development of a method of solution termed the inverse scattering transform (IST). The IST technique applies to continuous and discrete nonlinear Schrödinger (NLS) equations of scalar and vector type. This work presents a detailed mathematical study of the scattering theory, offers soliton solutions, and analyzes both scalar and vector soliton interactions. The authors provide advanced students and researchers with a thorough and self-contained presentation of the IST as applied to nonlinear Schrödinger systems.

Product Details

ISBN-13:
9780521534376
Publisher:
Cambridge University Press
Publication date:
04/28/2013
Series:
London Mathematical Society Lecture Note Series, #302
Edition description:
New Edition
Pages:
268
Product dimensions:
5.98(w) x 8.98(h) x 0.59(d)

Related Subjects

Table of Contents

1. Introduction; 2. Nonlinear schrödinger equation (NLS); 3. Integrable discrete nonlinear schrödinger equation (IDNSL); 4. Matrix nonlinear Schrödinger equation (MNLS); 5. Integrable discrete matrix NLS equation (IDMNLS); Appendix A. Summation by parts formula; Appendix B. Transmission of the Jost function through a localized potential; Appendix C. Scattering theory for the discrete Schrödinger equation; Appendix D. Nonlinear Schrödinger systems with a potential term; Appendix E. NLS systems in the limit of large amplitudes.

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