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Discrete and Continuous Nonlinear Schrödinger Systems

Discrete and Continuous Nonlinear Schrödinger Systems

Part of London Mathematical Society Lecture Note Series

  • Date Published: December 2003
  • availability: Available
  • format: Paperback
  • isbn: 9780521534376

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  • In recent years there have been important and far reaching developments in the study of nonlinear waves and a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field comes from the understanding of special waves called 'solitons' and the associated development of a method of solution to a class of nonlinear wave equations termed the inverse scattering transform (IST). Before these developments, very little was known about the solutions to such 'soliton equations'. The IST technique applies to both continuous and discrete nonlinear Schrödinger equations of scalar and vector type. Also included is the IST for the Toda lattice and nonlinear ladder network, which are well-known discrete systems. This book, first published in 2003, presents the detailed mathematical analysis of the scattering theory; soliton solutions are obtained and soliton interactions, both scalar and vector, are analyzed. Much of the material is not available in the previously-published literature.

    • 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: December 2003
    • 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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