Nonlinear dynamics of gap solitons in SOC-BECs trapped in a deformed honeycomb optical lattice

We investigate the nonlinear dynamics of gap solitons in Bose–Einstein condensates (BECs) with spin–orbit coupling (SOC) trapped in a deformed honeycomb optical lattice. The gap solitons are obtained by numerically solving the Gross–Pitaevskii equations using the Newton-Conjugate-Gradient method. In the semi-infinite gap, the strength of SOC positively influences the stability of gap solitons, whereas the Rabi coupling strength exerts an inhibitory effect on it. When both intra- and inter-component interactions are specified, the unipole gap solitons exhibit oscillatory dynamics of breather-like. Numerical calculations reveal that, with a constant Rabi coupling strength, the average period of oscillation of gap solitons changes regularly with variations in SOC strength. In the first gap, dipole gap solitons tend to collapse when either the SOC strength or the Rabi coupling strength is weak. However, we observe that unipole gap solitons demonstrate remarkable stability during their dynamical evolution. The results offer significant insights into the investigation of the local structural properties of nonlinear systems within BECs.