Interface solitons in one-dimensional locally-coupled lattice systems

TL;DR

This paper studies interface solitons in one-dimensional coupled lattice systems, analyzing their existence, stability, and bifurcations using variational approximation and numerical methods, with implications for optical waveguide arrays.

Contribution

It provides a comprehensive analysis of symmetric, antisymmetric, and asymmetric interface solitons in coupled lattice systems, including stability and bifurcation behaviors, using combined variational and numerical approaches.

Findings

Antisymmetric solitons exist across the entire parameter space.

Symmetric and asymmetric solitons exist below a critical coupling value.

Symmetric solitons undergo a supercritical bifurcation leading to stable asymmetric modes.

Abstract

Fundamental solitons pinned to the interface between two discrete lattices coupled at a single site are investigated. Serially and parallel-coupled identical chains (\textit{System 1} and \textit{System 2}), with the self-attractive on-site cubic nonlinearity, are considered in one dimension. In these two systems, which can be readily implemented as arrays of nonlinear optical waveguides, symmetric, antisymmetric and asymmetric solitons are investigated by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric solitons exist in the entire parameter space, while the symmetric and asymmetric modes can be found below some critical value of the coupling parameter. Numerical results confirm these predictions for the symmetric and asymmetric fundamental modes. The existence region of numerically found antisymmetric solitons is also limited by a certain value of the coupling parameter. The symmetric solitons are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric solitons, in both systems. The antisymmetric fundamental solitons, which may be stable or not, do not undergo any bifurcation. In bistability regions stable antisymmetric solitons coexist with either symmetric or asymmetric ones.