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arXiv · 1101.0501

Localization and delocalization of two-dimensional discrete solitons pinned to linear and nonlinear defects

Valeriy A. Brazhnyi·Boris A. Malomed
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Abstract

We study the dynamics of two-dimensional (2D) localized modes in the nonlinear lattice described by the discrete nonlinear Schr\"{o}dinger (DNLS) equation, including a local linear or nonlinear defect. Discrete solitons pinned to the defects are investigated by means of the numerical continuation from the anti-continuum limit and also using the variational approximation (VA), which features a good agreement for strongly localized modes. The models with the time-modulated strengths of the linear or nonlinear defect are considered too. In that case, one can temporarily shift the critical norm, below which localized 2D modes cannot exists, to a level above the norm of the given soliton, which triggers the irreversible delocalization transition.

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Valeriy A. Brazhnyi, Boris A. Malomed. 2011-01-03. Localization and delocalization of two-dimensional discrete solitons pinned to linear and nonlinear defects. https://doi.org/10.1103/physreve.83.016604

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