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© 2009

The Discrete Nonlinear Schrödinger Equation

Mathematical Analysis, Numerical Computations and Physical Perspectives

  • Authors
Book

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

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

About the authors

Panayotis G. Kevrekidis received a B.S. in Physics from University of Athens, an M.S., M.Phil and Ph.D in Physics from Rutgers University. After a post-doctoral year between Princeton University and Los Alamos National Lab, he joined the department of Mathematics and Statistics of UMass, Amherst where he is currently an Associate Professor. He has published more than 200 research papers and has received a CAREER award in Applied Mathematics from the U.S. National Science Foundation, as well as very recently a Humboldt Research Fellowship from the Alexander von Humboldt Foundation.

Bibliographic information

  • Book Title The Discrete Nonlinear Schrödinger Equation
  • Book Subtitle Mathematical Analysis, Numerical Computations and Physical Perspectives
  • Authors Panayotis G. Kevrekidis
  • Series Title Springer Tracts in Modern Physics
  • 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 Physics and Astronomy (R0)
  • Hardcover ISBN 978-3-540-89198-7
  • Softcover ISBN 978-3-642-24243-4
  • eBook ISBN 978-3-540-89199-4
  • Series ISSN 0081-3869
  • Series E-ISSN 1615-0430
  • Edition Number 1
  • Number of Pages XX, 416
  • Number of Illustrations 427 b/w illustrations, 85 illustrations in colour
  • Topics Quantum Physics
    Theoretical, Mathematical and Computational Physics
  • Buy this book on publisher's site
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Reviews

From the reviews:

“The collection contains 22 articles on various aspects of the discrete nonlinear Schrödinger equation … . The book provides a comprehensive and useful guide to the substantial mathematical and physical literature on the discrete nonlinear Schrödinger equation, both for novices and experts in the field.” (Karsten Matthies, Mathematical Reviews, Issue 2012 e)