Stationary and moving bright solitons in Bose-Einstein condensates with spin-orbit coupling in a Zeeman field

With the discovery of various matter wave solitons in spin-orbit-coupled Bose-Einstein condensates (BECs), exploring their properties has become increasingly significant. We mainly study stationary and moving bright solitons in spin-orbit-coupled spin-1 BECs with or without a Zeeman field. The bright solitons correspond to the plane wave (PW) and standing wave (SW) phases. With the assistance of single-particle energy spectrum, we obtain the existence domains of PW and SW solitons by analytical and numerical methods. The results indicate that the interaction between atoms is also a key factor determining the existence of solitons. In addition, we systematically discuss the stability domains of PW and SW solitons, and investigate the impact of different parameters on the stability domains. We find that PW solitons are unstable when the linear Zeeman effect reaches a certain threshold, and the threshold is determined by other parameters. The linear Zeeman effect also leads to the alternating distribution of stable and unstable areas of SW solitons, and makes SW solitons stably exist in the area with stronger ferromagnetism. Finally, we analyze the collision dynamics of different types of stable solitons.