The Discrete Nonlinear Schrödinger Equat
✍ Panayotis G. Kevrekidis (auth.)
📂 Library
📅 2009
🏛 Springer-Verlag Berlin Heidelberg
🌐 English
✦ LIBER ✦
📁
The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives
✍ Scribed by Panayotis G. Kevrekidis (auth.)
- Publisher
- Springer-Verlag Berlin Heidelberg
- Year
- 2009
- Tongue
- English
- Leaves
- 415
- Series
- Springer Tracts in Modern Physics 232
- Edition
- 1
- Category
- Library
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✦ Synopsis
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 of Contents
Front Matter....Pages i-xviii
Front Matter....Pages 1-1
General Introduction and Derivation of the DNLS Equation....Pages 3-9
The One-Dimensional Case....Pages 11-53
The Two-Dimensional Case....Pages 55-98
The Three-Dimensional Case....Pages 99-116
The Defocusing Case....Pages 117-141
Extended Solutions and Modulational Instability....Pages 143-152
MultiComponent DNLS Equations....Pages 153-171
Front Matter....Pages 173-173
Experimental Results Related to DNLS Equations....Pages 175-189
Numerical Methods for DNLS....Pages 191-203
The Dynamics of Unstable Waves....Pages 205-220
A Map Approach to Stationary Solutions of the DNLS Equation....Pages 221-233
Formation of Localized Modes in DNLS....Pages 235-247
Few-Lattice-Site Systems of Discrete Self-Trapping Equations....Pages 249-257
Surface Waves and Boundary Effects in DNLS Equations....Pages 259-275
Discrete Nonlinear Schrödinger Equations with Time-Dependent Coefficients ( Management of Lattice Solitons)....Pages 277-291
Exceptional Discretizations of the NLS: Exact Solutions and Conservation Laws....Pages 293-310
Solitary Wave Collisions....Pages 311-327
Related Models....Pages 329-351
DNLS with Impurities....Pages 353-368
Statistical Mechanics of DNLS....Pages 369-377
Front Matter....Pages 173-173
Traveling Solitary Waves in DNLS Equations....Pages 379-399
Decay and Strichartz Estimates for DNLS....Pages 401-412
Back Matter....Pages 1-3
✦ Subjects
Quantum Physics;Mathematical and Computational Physics
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