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The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives (Springer Tracts in Modern Physics, 232, Band 232) - Hardcover

Buch 145 von 227: Springer Tracts in Modern Physics

Kevrekidis, Panayotis G.

 
9783540891987: The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives (Springer Tracts in Modern Physics, 232, Band 232)
Hardcover
ISBN 10: 3540891986 ISBN 13: 9783540891987
Verlag: Springer, 2009

Inhaltsangabe

I Dimensions and Components.- General Introduction and Derivation of the DNLS Equation.- The One-Dimensional Case.- The Two-Dimensional Case.- The Three-Dimensional Case.- The Defocusing Case.- Extended Solutions and Modulational Instability.- MultiComponent DNLS Equations.- II Special Topics.- Experimental Results Related to DNLS Equations.- Numerical Methods for DNLS.- The Dynamics of Unstable Waves.- A Map Approach to Stationary Solutions of the DNLS Equation.- Formation of Localized Modes in DNLS.- Few-Lattice-Site Systems of Discrete Self-Trapping Equations.- Surface Waves and Boundary Effects in DNLS Equations.- Discrete Nonlinear Schr#x00F6;dinger Equations with Time-Dependent Coefficients ( of Lattice Solitons).- Exceptional Discretizations of the NLS: Exact Solutions and Conservation Laws.- Solitary Wave Collisions.- Related Models.- DNLS with Impurities.- Statistical Mechanics of DNLS.- Traveling Solitary Waves in DNLS Equations.- Decay and Strichartz Estimates for DNLS.

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Über die Autorin bzw. den Autor

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.

Von der hinteren Coverseite

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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Verlag
Springer
Erscheinungsdatum
2009
Sprache
Englisch
ISBN 10 
3540891986
ISBN 13 
9783540891987
Einband
Gebundene Ausgabe
Anzahl der Seiten
436
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