Discrete and Continuous Nonlinear Schrodinger Systems

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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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Editorial Reviews

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'… 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

  • ISBN-13: 9780521534376
  • Publisher: Cambridge University Press
  • Publication date: 4/28/2013
  • Series: London Mathematical Society Lecture Note Series, #302
  • Edition description: New Edition
  • Pages: 268
  • Product dimensions: 5.98 (w) x 8.98 (h) x 0.59 (d)

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.

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