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.