  We analyze a possibility of macroscopic quantum effects in the form of
coupled structural oscillations and shuttle motion of bright two-component
spin-orbit-coupled striped (one-dimensional, 1D) and semi-vortex
(two-dimensional, 2D) matter-wave solitons, under the action of linear mixing
(Rabi coupling) between the components. In 1D, the intrinsic oscillations
manifest themselves as flippings between spatially even and odd components of
striped solitons, while in 2D the system features periodic transitions between
zero-vorticity and vortical components of semi-vortex solitons. The
consideration is performed by means of a combination of analytical and
numerical methods.
