Moving Matter-Wave Solitons in Spin—Orbit Coupled Bose—Einstein Condensates**Supported by the National Natural Science Foundation of China under Grant Nos 11274255, 11305132 and 11475027, and the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No 20136203110001, and the Creation of Science and Technology of Northwest Normal University of China under Grant Nos NWNU-KJCXGC-03-48, NWNU-LKQN-12-12 and

Abstract

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.