  We studied the step dynamics during crystal sublimation and growth in the
limit of fast surface diffusion and slow kinetics of atom attachment-detachment
at the steps. For this limit we formulate a model free of the quasi-static
approximation in the calculation of the adatom concentration on the terraces at
the crystal surface. Such a model provides a relatively simple way to study the
linear stability of a step train in a presence of step-step repulsion and an
absence of destabilizing factors (as Schwoebel effect, surface electromigration
etc.). The central result is that a critical velocity of the steps in the train
exists which separates the stability and instability regimes. When the step
velocity exceeds its critical value the plot of these trajectories manifests
clear space and time periodicity (step density compression waves propagate on
the vicinal surface). This ordered motion of the steps is preceded by a
relatively short transition period of disordered step dynamics.
