Despite groundbreaking observations of supersolids in spin-orbit coupled Bose-Einstein condensates, the dynamics of spatially periodic density modulations that have emerged so far have been very unexplored. Here we investigate the dynamic behavior of density stripes in supersolid condensates subject to spin perturbations. We study how spin waves, in the form of crystal waves, affect the density profile of supersolids, inducing periodic oscillations and fringe orientations analytically in infinite systems and numerically in the presence of harmonic traps. is shown. Both of these features are within the scope of our current experiments. Our results show that this system is a paradigmatic supersolid, with superfluidity along with a fully dynamic crystal structure.

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