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The Discrete Nonlinear Schrödinger Equation

Mathematical Analysis, Numerical Computations and Physical Perspectives

  • Book
  • © 2009

Overview

  • First book on nonlinear Schrödinger equation
  • Systematical treatment and derivation of the nonlinear Schrödinger equation
  • Establishes connections to the application of this theory to spacial lattice dimensions, non-linearities, modulation, and wave solutions
  • Written for researchers and graduate students
  • Includes supplementary material: sn.pub/extras

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

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About this book

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.

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Keywords

Table of contents (22 chapters)

  1. General Theory

  2. I Dimensions and Components

  3. Special Topics

  4. II Special Topics

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)

About the author

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

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2009

  • Hardcover ISBN: 978-3-540-89198-7Published: 17 July 2009

  • Softcover ISBN: 978-3-642-24243-4Published: 29 November 2011

  • eBook ISBN: 978-3-540-89199-4Published: 07 July 2009

  • 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

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