The Discrete Nonlinear Schrödinger Equation
Mathematical Analysis, Numerical Computations and Physical Perspectives
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Beschreibung
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.
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
Autor*in
Panayotis G. Kevrekidis
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DNLS Nonlinear science Solitary waves calculus differential equation numerical methods
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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)()