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

TL;DR

This paper investigates the behavior of two-dimensional discrete solitons in nonlinear lattices with defects, analyzing their localization, delocalization, and the effects of time-modulated defect strengths using numerical and variational methods.

Contribution

It introduces a combined numerical and variational approach to study 2D solitons pinned to defects, including the effects of time-modulated defect strengths on localization.

Findings

Discrete solitons can be pinned to linear or nonlinear defects.

Time modulation of defect strengths can induce irreversible delocalization transitions.

The variational approximation agrees well with numerical results for strongly localized modes.

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.