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

Statical Structures of the BCS-like Holographic Superfluid in AdS4 Spacetime