Dynamics of multiple solitons in helicoidal spin-orbit coupling Bose–Einstein condensates

In this paper, we focus on solitons with periodic evolution in the helicoidal spin-orbit coupling Bose–Einstein condensates (SOC-BEC) system. We use a gauge transformation to obtain solitons that coexist in two energy bands without the Zeeman effect. More stripes appear in the solitons as the SOC strength increases. The period oscillation of soliton evolution is because the solitons emerge from states in the different energy levels simultaneously. The influence of the Zeeman effect on the multi-hump solitons occupying two energy levels is numerically analyzed. We also discuss the collisions of the multi-hump solitons and give the conditions for elastic and inelastic collisions. Our study may shed light on an alternative way to detect the energy level differences for the SOC-BEC system.