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We demonstrate the formation of multi-peak three-component stationary stripevector solitons in a quasi-one-dimensional spin-orbit-coupled hyper-fine spin$F = 1$ polar Bose-Einstein condensate. The present investigation is carriedout through a numerical solution by imaginary-time propagation and an analyticvariational approximation of the underlying mean-field Gross-Pitaevskiiequation. Simple analytic results for energy and component densities were foundto be in excellent agreement with the numerical results for solitons with morethan 100 pronounced maxima and minima. The vector solitons are one of the twotypes: dark-bright-dark or bright-dark-bright. In the former a maximum densityin component $ F_z = 0 $ at the center is accompanied by a zero in components$F_z = \pm 1$. The opposite happens in the latter case. The vector solitons aredemonstrated to be mobile and dynamically stable. The collision between twosuch vector solitons is found to be quasi elastic at large velocities with theconservation of total density of each vector soliton. However, at very smallvelocity, the collision is inelastic with a destruction of the initial vectorsolitons. It is possible to observe and study the predicted SO-coupled vectorsolitons in a laboratory.

Stable multi-peak vector solitons in spin-orbit coupled spin-1 polar condensates