Localized modes in mini-gaps opened by periodically modulated intersite coupling in two-dimensional nonlinear lattices

TL;DR

This paper investigates how periodic modulation of intersite coupling in 2D nonlinear lattices creates mini-gaps in the spectrum, enabling the formation of stable localized modes like solitons and breathers within these mini-gaps.

Contribution

It demonstrates the existence and stability of various localized modes in mini-gaps caused by periodic intersite coupling modulation in 2D nonlinear lattices.

Findings

Stable single-peak solitons exist in certain mini-gap regions.

Composite multi-peak solitons and breathers can form and are stable or transform into breathers.

Periodic modulation effectively creates new localized modes in the mini-gaps.

Abstract

Spatially periodic modulation of the intersite coupling in two-dimensional (2D) nonlinear lattices modifies the eigenvalue spectrum by opening mini-gaps in it. This work aims to build stable localized modes in the new bandgaps. Numerical analysis shows that single-peak and composite two- and four-peak discrete static solitons and breathers emerge as such modes in certain parameter areas inside the mini-gaps of the 2D superlattice induced by the periodic modulation of the intersite coupling along both directions.The single-peak solitons and four-peak discrete solitons are stable in a part of their existence domain, while unstable stationary states (in particular, two-soliton complexes) may readily transform into robust localized breathers.