  We report on the existence and stability of freely moving solitons in a
spatially inhomogeneous Bose- Einstein condensate with helicoidal spin-orbit
(SO) coupling. In spite of the periodically varying parameters, the system
allows for the existence of stable propagating solitons. Such states are found
in the rotating frame, where the helicoidal SO coupling is reduced to a
homogeneous one. In the absence of the Zeeman splitting, the coupled
Gross-Pitaevskii equations describing localized states feature many properties
of the integrable systems. In particular, four-parametric families of solitons
can be obtained in the exact form. Such solitons interact elastically. Zeeman
splitting still allows for the existence of two families of moving solitons,
but makes collisions of solitons inelastic.
