  We investigate the spatiotemporal dynamics of cavity solitons in a broad area
vertical-cavity surface-emitting laser with saturable absorption subjected to
time-delayed optical feedback. Using a combination of analytical, numerical and
path continuation methods we analyze the bifurcation structure of stationary
and moving cavity solitons and identify two different types of traveling
localized solutions, corresponding to slow and fast motion. We show that the
delay impacts both stationary and moving solutions either causing drifting and
wiggling dynamics of initially stationary cavity solitons or leading to
stabilization of intrinsically moving solutions. Finally, we demonstrate that
the fast cavity solitons can be associated with a lateral mode-locking regime
in a broad-area laser with a single longitudinal mode.
