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General Introduction and Derivation of the DNLS Equation

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The Discrete Nonlinear Schrödinger Equation

Part of the book series: Springer Tracts in Modern Physics ((STMP,volume 232))

The discrete nonlinear Schrödinger (DNLS) equation is, arguably, one of the most fundamental nonlinear lattice dynamical models. On the one hand, this is due to its being the prototypical discretization for its famous and integrable continuum sibling, namely the nonlinear Schrödinger (NLS) equation [1, 8] which has a wide range of applications; it is the relevant dispersive envelope wave model for describing the electric field in optical fibers [13, 34], for the self-focusing and collapse of Langmuir waves in plasma physics [5, 6], or for the description of freak waves (the so-called rogue waves) in the ocean [7]. On the other hand, the DNLS is a model of particular physical interest in its own right, with a diverse host of areas where it is of physical interest; see, e.g., [38] for a relevant review. We mention a brief outline of these areas below.

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  1. Dept. Mathematics & Statistics, University of Massachussetts, Amherst, Amherst, MA 01003, USA

    Prof.Dr Panayotis G. Kevrekidis

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  1. Prof.Dr Panayotis G. Kevrekidis
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Kevrekidis, P.G. (2009). General Introduction and Derivation of the DNLS Equation. In: The Discrete Nonlinear Schrödinger Equation. Springer Tracts in Modern Physics, vol 232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89199-4_1

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  • DOI: https://doi.org/10.1007/978-3-540-89199-4_1

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