Bright Discrete Solitons in Spatially Modulated DNLS Systems

TL;DR

This paper investigates bright discrete solitons in spatially modulated DNLS systems, analyzing their existence, stability, and dynamics using the anti-continuum limit, revealing enhanced robustness and broader solution profiles.

Contribution

It introduces a systematic analysis of bright solitons in inhomogeneous DNLS systems starting from the anti-continuum limit, highlighting stability and bifurcation properties.

Findings

Solutions with broader support are more stable and have wider existence intervals.

Eigenvalue predictions match numerical stability analysis.

Solutions tend to broaden dynamically, supporting their robustness.

Abstract

In the present work, we revisit the highly active research area of inhomogeneously nonlinear defocusing media and consider the existence, spectral stability and nonlinear dynamics of bright solitary waves in them. We use the anti-continuum limit of vanishing coupling as the starting point of our analysis, enabling in this way a systematic characterization of the branches of solutions. Our stability findings and bifurcation characteristics reveal the enhanced robustness and wider existence intervals of solutions with a broader support, culminating in the "extended" solution in which all sites are excited. Our eigenvalue predictions are corroborated by numerical linear stability analysis. Finally, the dynamics also reveal a tendency of the solution profiles to broaden, in line with the above findings. These results pave the way for further explorations of such states in discrete systems, including in higher dimensional settings.