  We investigate in detail the m^{2}=0 Abelian Higgs model in AdS4, which is
considered as the holographic dual of the most BCS-like superfluid. In
homogeneous and isotropic superfluid solutions, we calculate the sound speeds,
square of which approaches to 1/2 with increasing chemical potential (lowering
temperature). Then we present the single dark soliton solutions, which becomes
thinner with increasing chemical potential. For the first time, we also find
the interesting double and triple dark soliton solutions, which is unexpected
and shows the possibility of more complicated static configurations. Finally,
we investigate vortex solutions. For winding number n=1, the vortex becomes
thinner with increasing chemical potential. At a given chemical potential, with
increasing winding number, firstly the vortex becomes bigger and the charge
density depletion becomes larger, then the charge density depletion settles
down at a certain value and the growth of the vortex size is found to obey a
scaling symmetry.
