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The Discrete Nonlinear Schrödinger Equation [electronic resource] :Mathematical Analysis, Numerical Computations and Physical Perspectives / by Panayotis G. Kevrekidis.

by Kevrekidis, Panayotis G [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Springer Tracts in Modern Physics: 232Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.Description: online resource.ISBN: 9783540891994.Subject(s): Physics | Quantum theory | Mathematical physics | Physics | Quantum Physics | Mathematical and Computational PhysicsOnline resources: Click here to access online
Contents:
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 Schrödinger 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.
In: Springer eBooksSummary: 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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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 Schrödinger 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.

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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