Discrete and Continuous Nonlinear Schrà dinger Systems

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.

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.