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Springer Tracts in Modern Physics

The Discrete Nonlinear Schrödinger Equation

Mathematical Analysis, Numerical Computations and Physical Perspectives

Authors: Kevrekidis, Panayotis G.

  • 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
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eBook $249.00
price for USA (gross)
valid through October 16, 2017
  • ISBN 978-3-540-89199-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $319.00
price for USA
valid through October 16, 2017
  • ISBN 978-3-540-89198-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $319.00
price for USA
  • ISBN 978-3-642-24243-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.

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.

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)

Table of contents (22 chapters)

  • General Introduction and Derivation of the DNLS Equation

    Kevrekidis, Panayotis G.

    Pages 3-9

  • The One-Dimensional Case

    Kevrekidis, Panayotis G.

    Pages 11-53

  • The Two-Dimensional Case

    Kevrekidis, Panayotis G.

    Pages 55-98

  • The Three-Dimensional Case

    Kevrekidis, Panayotis G.

    Pages 99-116

  • The Defocusing Case

    Kevrekidis, Panayotis G.

    Pages 117-141

Buy this book

eBook $249.00
price for USA (gross)
valid through October 16, 2017
  • ISBN 978-3-540-89199-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $319.00
price for USA
valid through October 16, 2017
  • ISBN 978-3-540-89198-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $319.00
price for USA
  • ISBN 978-3-642-24243-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Discrete Nonlinear Schrödinger Equation
Book Subtitle
Mathematical Analysis, Numerical Computations and Physical Perspectives
Authors
Series Title
Springer Tracts in Modern Physics
Series Volume
232
Copyright
2009
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-89199-4
DOI
10.1007/978-3-540-89199-4
Hardcover ISBN
978-3-540-89198-7
Softcover ISBN
978-3-642-24243-4
Series ISSN
0081-3869
Edition Number
1
Number of Pages
XX, 416
Number of Illustrations and Tables
427 b/w illustrations, 85 illustrations in colour
Topics