  We show that the decay of sinusoidal ripples on crystal surfaces, where mass
transport is limited by the attachment and detachment of atoms at the
step-edges, is remarkably different from the decay behavior that has been
reported until now. Unlike the decreasing or at most constant rate of amplitude
decay of sinusoidal profiles observed in earlier work, we find that the decay
rate increases with decreasing amplitude in this kinetic regime. The rate of
shape invariant amplitude relaxation is shown to be inversely proportional to
both the square of the wavelength and the current amplitude. We have also
carried out numerical simulations of the relaxation of realistic sputter
ripples.
