Dark gap soliton families in coupled nonlinear Schrödinger equations with linear lattices

We demonstrate that two types of dark gap soliton families, the fundamental dark solitons and the dark soliton clusters, can be stabilized in coupled nonlinear Schr & ouml;dinger equations (NLSEs) with linear lattices. Two types of coupled NLSEs are investigated, those with identical lattices and those with different lattices. In the latter case, one component features a monochromatic linear lattice, while the other features a bichromatic linear lattice. For coupled NLSEs with the same lattices, the soliton profiles are nearly identical, with both components exhibiting monochromatic backgrounds. In contrast, for coupled NLSEs with different lattices, the profiles differ significantly: one component has a monochromatic background, while the other has a bichromatic background. The stability domains of these dark soliton families are determined by the method of linear stability analysis, and also confirmed by direct numerical simulations.