Discrete and Continuous Nonlinear Schr¶dinger Systems

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Paperback | 9 March 2004

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268 Pages

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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 Schr¶dinger 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, first published in 2003, 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.

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'... this valuable book provides a detailed and self-contained presentation of an extremely important tool used in the study of NLS systems.' EMS Newsletter

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Introduction
Nonlinear schr¶dinger equation (NLS)
Integrable discrete nonlinear schr¶dinger equation (IDNSL)
Matrix nonlinear Schr¶dinger equation (MNLS)
Integrable
Integrable discrete matrix NLS equation (IDMNLS)
Summation by parts formula
Transmission of the Jost function through a localized potential
Scattering theory for the discrete Schr¶dinger equation
Nonlinear Schr¶dinger systems with a potential term
NLS systems in the limit of large amplitudes
Table of Contents provided by Publisher. All Rights Reserved.

Discrete and Continuous Nonlinear Schr¶dinger Systems

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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