The Discrete Nonlinear Schrödinger Equation

Mathematical Analysis, Numerical Computations and Physical Perspectives
2009
ISBN: 978-3-540-89198-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 232, 416 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 896 g

Reihe: Springer Tracts in Modern Physics

Adventures of nonlinear science were perhaps most notably seeded at the Los Alamos National Laboratory (LANL) over half a century ago with the fundamental questionsofenergyequipartitioninnonlinearsystems, astheywereposedbyFermi, Pasta, and Ulam. At the time, probably little could be imagined of the far-reaching implications that the studies of nonlinear phenomena would have, continuing to expandtothisday.TheGinzburg–Landautheoryofsuperconductivityandtheord- parameter descriptions of super uidity, the “soliton revolution” through the works of Zabusky and Kruskal on the KdV equation and the subsequent widespread - plicationsof the nonlinear Schrodi ¨ ngerequation in optical bers and Bose–Einstein condensates,the developmentsof bifurcationtheory and chaotic dynamicsand their widespread applicationsfrom climate and geophysics,to biological phenomenaand chemical kineticsare only a few of the multiple arenas in which nonlineardynamics have emerged as the appropriate description of important physical systems. I well remember my own early days of nonlinear science appreciation, rst at Cornell University in the early 1970s and then at Los Alamos where we began the Center for Nonlinear Studies (CNLS) in 1980. These were years marked by interdisciplinary discovery and by the recognition that many nonlinear equations have an inherent ability to exhibit both coherence and chaos – the beginnings of our appreciation today of spatio-temporal complexity and the functional role that this plays in multiple branches of science, technology, and engineering.

Zielgruppe

Research

Autoren/Hrsg.

Kevrekidis, Panayotis G.

Fachgebiete

• Naturwissenschaften Physik Quantenphysik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

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.

Über Autor(innen)

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.