Motivated by the prospect of Bardeen-Cooper-Schrieffer (BCS) pairing in cold
fermionic gases we analyze the superfluid phase of 3 fermionic flavors in the
attractive Hubbard model. We show that there are several low--lying collective
pairing modes and investigate their damping due to the partially gapless nature
of the single-particle spectrum. Furthermore we analyze how these modes show up
in the density response of the system. Apart from the Anderson-Bogoliubov phase
mode of the pairing between two flavors, the dynamical structure factor
contains signatures of the gapless third flavor. This picture is found to be
robust against perturbations that break the global SU(3)-symmetry of the
Hamiltonian.Comment: 13 pages, 6 figure