Nonlinear lattice waves in heterogeneous media
T.V. Laptyeva, M.V. Ivanchenko, and S. Flach
TL;DR
This paper reviews recent advances in understanding how nonlinear lattice waves behave in heterogeneous media, focusing on localization phenomena and the effects of nonlinearity on wave dynamics.
Contribution
It provides a comprehensive overview of the interplay between nonlinearity and localization in heterogeneous media, highlighting recent progress and universal features of wave spreading.
Findings
Localization can be preserved or destroyed by nonlinear effects.
Universal features observed in spreading wave packets.
Nonlinear diffusion equations relate to wave dynamics.
Abstract
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.
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