The dynamics of strongly interacting trapped dilute Fermi gases (dilute in
the sense that the range of interatomic potential is small compared with
inter-particle spacing) is investigated in a single-equation approach to the
time-dependent density-functional theory. Our results are in good agreement
with recent experimental data in the BCS-BEC crossover regime. It is also shown
that the calculated corrections to the hydrodynamic approximation may be
important even for systems with a rather large number of atoms.Comment: Resubmitted to PRA in response to referee's comments. Abstract is
changed. Added new figure