Discrete and Continuous Nonlinear Schrödinger Systems (London Mathematical Society Lecture Note Series)
Publisher: Cambridge University Press
Published: January 19, 2004
Language: eng
Format: Paperback
Number of pages: 268
ISBN-13: 9780521534376
Subjects: Applied mathematics; Differential Equations; Theoretical methods; Waves & Wave Mechanics; Mathematics; General; Science/Mathematics; Schrèodinger equation; Nonlinear theories; Mathematics / General; Linear Programming; Inverse scattering transform; Schrodinger equation
First sentence: Ever since the observation of the "great wave of translation" in water waves, by J. Scott Russell in 1834 [146, 147] while he rode on horseback near a narrow canal in Edinburgh, localized (nonoscillatory) solitary waves have been known to researchers studying wave dynamics.
Description: 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 Schrḏinger (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 Schrḏinger systems.