Gap solitons of spin–orbit-coupled Bose–Einstein condensates in PT periodic potential

We numerically investigate the gap solitons in Bose–Einstein condensates(BECs)with spin–orbit coupling(SOC)in the parity–time(PT)-symmetric periodic potential.We find that the depths and periods of the imaginary lattice have an important influence on the shape and stability of these single-peak gap solitons and double-peak gap solitons in the first band gap.The dynamics of these gap solitons are checked by the split-time-step Crank–Nicolson method.It is proved that the depths of the imaginary part of the PT-symmetric periodic potential gradually increase,and the gap solitons become unstable.But the different periods of imaginary part hardly affect the stability of the gap solitons in the corresponding parameter interval.