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

Abstract

We study the dynamics of two-dimensional (2D) localized modes in the nonlinear lattice described by the discrete nonlinear Schrödinger (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.

arXiv comment7 pages, 11 figures

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Cited by in corpus (6)

• Discrete solitons in self-defocusing systems with $\mathcal{P}\mathcal{T}$-symmetric defects
• Two-dimensional intra-band solitons in lattice potentials with local defects and self-focusing nonlinearity
• Interface solitons in locally linked two-dimensional lattices
• Dragging two-dimensional discrete solitons by moving linear defects
• Enhanced mobility of discrete solitons in anisotropic two-dimensional waveguide arrays with modulated separations
• Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices