  Despite ground-breaking observations of supersolidity in spin-orbit-coupled
Bose-Einstein condensates, until now the dynamics of the emerging spatially
periodic density modulations has been vastly unexplored. Here, we demonstrate
the nonrigidity of the density stripes in such a supersolid condensate and
explore their dynamic behavior subject to spin perturbations. We show both
analytically in infinite systems and numerically in the presence of a harmonic
trap how spin waves affect the supersolid's density profile in the form of
crystal waves, inducing oscillations of the periodicity as well as the
orientation of the fringes. Both these features are well within reach of
present-day experiments. Our results show that this system is a paradigmatic
supersolid, featuring superfluidity in conjunction with a fully dynamic
crystalline structure.
