Nonlinear lattice waves in heterogeneous media

We review recent progress in the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-Andre localization for quasiperiodic potentials. Additional nonli...

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Bibliographic Details
Published in:arXiv.org 2014-07
Main Authors: Laptyeva, T V, Ivanchenko, M V, Flach, S
Format: Article
Language:English
Subjects:
Anderson localization
Localization
Mathematical analysis
Nonlinear dynamics
Nonlinear equations
Wave equations
Wave packets
Online Access:Get full text
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Summary:We review recent progress in the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-Andre localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations.
ISSN:2331-8422
DOI:10.48550/arxiv.1407.1441