Dark–bright discrete solitons: A numerical study of existence, stability and dynamics

In the present work, we numerically explore the existence and stability properties of different types of configurations of dark–bright solitons, dark–bright soliton pairs and pairs of dark–bright and dark solitons in discrete settings, starting from the anti-continuum limit. We find that while single discrete dark–bright solitons have similar stability properties to discrete dark solitons, their pairs may only be stable if the bright components are in phase and are always unstable if the bright components are out of phase. Pairs of dark–bright solitons with dark ones have similar stability properties as individual dark or dark–bright ones. Lastly, we consider collisions between dark–bright solitons and between a dark–bright one and a dark one. Especially in the latter and in the regime where the underlying lattice structure matters, we find a wide range of potential dynamical outcomes depending on the initial soliton speed.

Research highlights
► Dark–bright solitons are found in coupled discrete NLS equations.
► Single dark–bright discrete solitons have similar stability properties as dark ones.
► Dark–bright soliton pairs are unstable if the bright components are out of phase.
► Bright components repel (attract) when they are in (out of) phase.