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The Discrete Nonlinear Schrödinger Equation

Mathematical Analysis, Numerical Computations and Physical Perspectives

  • Authors
  • Panayotis G. Kevrekidis

Part of the Springer Tracts in Modern Physics book series (STMP, volume 232)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. General Theory

    1. Front Matter
      Pages 1-1
    2. Panayotis G. Kevrekidis
      Pages 11-53
    3. Panayotis G. Kevrekidis
      Pages 55-98
    4. Panayotis G. Kevrekidis
      Pages 99-116
    5. Panayotis G. Kevrekidis
      Pages 117-141
    6. Panayotis G. Kevrekidis
      Pages 143-152
    7. Panayotis G. Kevrekidis
      Pages 153-171
  3. Special Topics

    1. Front Matter
      Pages 173-173
    2. Mason A. Porter
      Pages 175-189
    3. Kody J. H. Law, Panayotis G. Kevrekidis
      Pages 191-203
    4. Kody J.H. Law, Q. Enam Hoq
      Pages 205-220
    5. Ricardo Carretero-González
      Pages 221-233
    6. Panayotis G. Kevrekidis
      Pages 235-247
    7. Ying-Ji He, Boris A. Malomed
      Pages 259-275
    8. Sergey V. Dmitriev, Dimitri J. Frantzeskakis
      Pages 311-327
    9. Boris A. Malomed
      Pages 329-351
    10. Jesús Cuevas, Faustino Palmero
      Pages 353-368
    11. Panayotis G. Kevrekidis
      Pages 369-377
    12. Alan R. Champneys, Vassilis M. Rothos, Thomas R.O. Melvin
      Pages 379-399
    13. Atanas Stefanov
      Pages 401-412
  4. Back Matter
    Pages 1-3

About this book

Introduction

This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes. It contains an introduction to the model, its systematic derivation and its connection to applications, a subsequent analysis of the existence and the stability of fundamental nonlinear structures in 1, 2 and even 3 spatial lattice dimensions. It also covers the case of defocusing nonlinearities, the modulational instabilities of plane wave solutions, and the extension to multi-component lattices. In addition, it features a final chapter on special topics written by a wide array of experts in the field, addressing through short reviews, areas of particular recent interest.

Keywords

DNLS Nonlinear science Solitary waves calculus differential equation numerical methods

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-89199-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-540-89198-7
  • Online ISBN 978-3-540-89199-4
  • Series Print ISSN 0081-3869
  • Series Online ISSN 1615-0430
  • Buy this book on publisher's site