Dark gap quantum droplets in linear lattices

We study the existence of dark gap quantum droplet (DGQD) families in the nonlinear Schr & ouml;dinger equation with linear lattices, including both individual DGQDs and their clusters. Two types of linear lattices are studied in this work, monochromatic and bichromatic. The backgrounds of these families in bichromatic lattices differ from those in monochromatic lattices, being composed of two lattices instead of one. The stability of individual DGQDs is established by the linear stability analysis, and verified by direct numerical simulations. The stability domains of DGQD clusters are significantly narrower than those of individual DGQDs in monochromatic linear lattices. In contrast, for bichromatic linear lattices, the stability domains of DGQD clusters are nearly identical to those of individual DGQDs. Finally, we identify the domains of strongly and weakly unstable oscillation regimes of DGQD clusters, based on the values of the linear instability growth rate.