Composite solitons in spin–orbit-coupled Bose–Einstein condensates within optical lattices

We demonstrate that the two-component model of Bose–Einstein condensates (BECs) trapped in an optical lattice with the spin–orbit Rashba coupling and cubic repulsive interactions gives rise to gap solitary complexes of three types. The first type is the fundamental–fundamental soliton (FFS), with a fundamental soliton in both components; the second is the fundamental–dipole soliton (FDS), with a fundamental soliton in one component and a dipole soliton in the other; and the third is the dual-hump–dual-hump soliton (DHDHS), with a dual-hump soliton in both components. We study two types of fundamental solitons, namely, the single-hump and the three-hump ones. We establish that the first and second components of FFS and DHDHS in our model are mirror-symmetric about the y-axis. The first component of FDS displays the left–right symmetry, while the second component displays the rotational symmetry about the origin. We also discover that the stability domains of FFS and FDS in both the first and second band gaps are large, lending credence to their stability. This work advances the understanding of the rather complicated behavior of BECs in optical lattices and opens avenues for experimental verification of these gap soliton structures.