Discrete and Continuous Nonlinear Schrödinger Systems
Discrete and Continuous Nonlinear Schrödinger Systems by M. J. Ablowitz, published by Cambridge University Press in 2004, is a comprehensive exploration of nonlinear waves, particularly focusing on soliton equations. This first edition spans 257 pages and is presented in English. The book delves into significant advancements in the study of nonlinear wave equations, emphasizing the inverse scattering transform (IST) method, which has become essential in understanding these complex systems.
Readers will find a thorough, self-contained presentation of the IST as it applies to continuous and discrete nonlinear Schrödinger equations. The text addresses the importance of these equations in various physical applications, including nonlinear optics and fluid dynamics. By detailing the method of solution and its implications, this book serves as a valuable resource for those interested in mathematics, differential equations, and mathematical analysis, providing insights that are not readily available in existing literature.
Official synopsis Publisher
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.
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