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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.
Table des matières
1. General Introduction and Derivation of the DNLS Equation.- 2. The One-Dimensional Case.- 3. The Two-Dimensional Case.- 4. The Three-Dimensional Case.- 5. The Defocusing Case.- 6. Extended Solutions and Modulational Instability.- 7. Multi-Component Solitary Waves.- 8. Experimental Results Related to DNLS Equations.- 9. Numerical Methods for DNLS.- 10. The Dynamics of Unstable Waves.- 11. A Map Approach to Stationary Solutions of the DNLS Equation.- 12. Formation of Localized Modes in DNLS.- 13. Few-lattice-site Systems of Discrete Self-Trapping Equations.- 14. Surface Waves and Boundary Effects in DNLS Equations.- 15. Discrete Nonlinear Schrödinger Equations with Time-Dependent Coefficients.- 16. Exceptional Discretizations of the NLS.- 17. Solitary Wave Collisions.- 18. Related Models.- 19. DNLS with Impurities.- 20. Statistical Mechanics of DNLS.- 21. Traveling Solitary Waves in DNLS Equations.- Decay and Strichartz Estimates for DNLS.
A propos de l'auteur
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.
Résumé
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.
Texte suppl.
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)
Commentaire
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)
