Interface solitons in locally linked two-dimensional lattices

TL;DR

This paper explores the existence, stability, and dynamics of interface solitons in two coupled 2D lattices, revealing bifurcations and coexistence of different soliton modes through analytical and numerical methods.

Contribution

It introduces a new model of coupled 2D lattices with localized linking, analyzing symmetric, antisymmetric, and asymmetric solitons using variational and numerical approaches.

Findings

Antisymmetric solitons exist across all parameters.

Symmetric and asymmetric modes appear below a critical coupling.

Bistability of antisymmetric with symmetric or asymmetric solitons occurs.

Abstract

Existence, stability and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel 2D (two-dimensional) lattices, are investigated. The system with the on-site cubic self-focusing nonlinearity is modeled by the pair of discrete nonlinear Schr\"{o}dinger equations linearly coupled at the single site. Symmetric, antisymmetric and asymmetric complexes are constructed by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric soliton complexes exist in the entire parameter space, while the symmetric and asymmetric modes can be found below a critical value of the coupling parameter. Numerical results confirm these predictions. The symmetric complexes are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric modes. The antisymmetric complexes are subject to oscillatory and exponentially instabilities in narrow parametric regions. In bistability areas, stable antisymmetric solitons coexist with either symmetric or asymmetric ones.