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Discrete and Continuous Nonlinear Schrödinger Systems

Discrete and Continuous Nonlinear Schrödinger Systems

$102.00 (C)

Part of London Mathematical Society Lecture Note Series

  • Date Published: January 2004
  • availability: Available
  • format: Paperback
  • isbn: 9780521534376

$ 102.00 (C)

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About the Authors
  • 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.

    • Solution of class of physically interesting nonlinear Schrödinger (NLS) equations
    • Fills important gap in field literature, covering nonlinear Schrödinger systems and discrete soliton systems in mathematical detail
    • Careful, concrete and systematic analysis of key aspects of NLS vector soliton interactions
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    Reviews & endorsements

    '… 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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    Product details

    • Date Published: January 2004
    • format: Paperback
    • isbn: 9780521534376
    • length: 268 pages
    • dimensions: 224 x 150 x 15 mm
    • weight: 0.4kg
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Nonlinear schrödinger equation (NLS)
    3. Integrable discrete nonlinear schrödinger equation (IDNSL)
    4. Matrix nonlinear Schrödinger equation (MNLS)
    5. Integrable discrete matrix NLS equation (IDMNLS)
    Appendix A. Summation by parts formula
    Appendix B. Transmission of the Jost function through a localized potential
    Appendix C. Scattering theory for the discrete Schrödinger equation
    Appendix D. Nonlinear Schrödinger systems with a potential term
    Appendix E. NLS systems in the limit of large amplitudes.

  • Authors

    M. J. Ablowitz, University of Colorado, Boulder

    B. Prinari, Università degli Studi di Lecce, Italy

    A. D. Trubatch, United States Military Academy

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