From a three-dimensional (3D) nonlinear density functional equation which describe appropriately the stationary and non-stationary states of a trapped superfluid (SF) of bosons or fermions atoms, we develop one- (1D) and two-dimensional (2D) effective equations to describe a trapped cigar- and disk-shaped SF respectively. The numerical solution of 1D and 2D equations to describe a SF for any scattering length has some advantages. It is simpler and employs smaller computational time, opposite to the Monte Carlo simulation or other microscopic formulation for many particles whose solutions are difficult to find. The results obtained from 1D and 2D equations are in good agreement with the solution of the full 3D equation for trapped cigar- and disk-shaped SF for any value of the atomic interaction. This system 1D and 2D can be used for study Anderson localization in random potentials. Also to let study the properties of a Fermi SF in different regions of interaction. Besides to study system in lower dimensions is very important for construction of any theory to explain the behavior of SF of ultra-cold atoms in mix-systems which live in different dimensions. Recent experimental evidences showed which these systems with mix-dimensions exist.
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