Moving Matter-Wave Solitons in Spin–Orbit Coupled Bose–Einstein Condensates

We investigate the moving matter-wave solitons in spin–orbit coupled Bose–Einstein condensates (BECs) by a perturbation method. Starting with the one-dimensional Gross–Pitaevskii equations, we derive a new KdV-like equation to which an approximate solution is obtained by assuming weak Raman coupling and strong spin–orbit coupling. The derivation of the KdV-like equation may be useful to understand the properties of solitons excitation in spin–orbit coupled BECs. We find different types of moving solitons: dark–bright, bright–bright and dark–dark solitons. Interestingly, moving dark–dark soliton for attractive intra- and inter-species interactions is found, which depends on the Raman coupling. The amplitude and velocity of the moving solitons strongly depend on the Raman coupling and spin–orbit coupling.