Discrete and Continuous Nonlinear Schrdinger Systems (Paperback)

B. Prinari

ISBN 10: 0521534372 / ISBN 13: 9780521534376

Published by Cambridge University Press, Cambridge, 2003

About this Item

Paperback. In recent years there have been important and far reaching developments in the study of nonlinear waves and a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field comes from the understanding of special waves called 'solitons' and the associated development of a method of solution to a class of nonlinear wave equations termed the inverse scattering transform (IST). Before these developments, very little was known about the solutions to such 'soliton equations'. The IST technique applies to both continuous and discrete nonlinear Schrodinger equations of scalar and vector type. Also included is the IST for the Toda lattice and nonlinear ladder network, which are well-known discrete systems. This book presents the detailed mathematical analysis of the scattering theory; soliton solutions are obtained and soliton interactions, both scalar and vector, are analyzed. Much of the material is not available in the previously-published literature. In this book, the detailed mathematical analysis of the scattering theory is presented, soliton solutions are obtained and soliton interactions, both scalar and vector, are analyzed. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9780521534376

Bibliographic Details

• Title: Discrete and Continuous Nonlinear Schrdinger Systems (Paperback)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2003
• Language: English
• ISBN 10: 0521534372
• ISBN 13: 9780521534376
• Binding: Paperback
• Condition: new

About this title

Synopsis

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.

Book Description

During the past 30 years there have been important and far reaching developments in the study of nonlinear waves including "soliton equations", a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field can be traced to the understanding of certain special stable, localized waves called solitons and the associated development of a method of solution to a class of nonlinear wave equations. Prior to these developments very little was known about the solutions to these equations.The method of solution, termed the inverse scattering transform (IST), applies to a class of continuous and discrete nonlinear Schrödinger (NLS) equations. NLS equations are of particular interest because they arise in many important physical applications, such as nonlinear optics, fluid dynamics and statistical physics. Many of the details of the IST presented in this book are not available in the previously-published literature. This book provides a thorough, self-contained presentation of the IST as applied to NLS systems.