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Discrete and Continuous Nonlinear Schrödinger Systems

✍ Scribed by M. J. Ablowitz, B. Prinari, A. D. Trubatch

Publisher
Cambridge University Press
Year
2004
Tongue
English
Leaves
268
Series
London Mathematical Society Lecture Note Series
Category
Library
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✦ 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.

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