  We obtain a self-dual formulation of the conventional nonlinear Schr\"odinger
equation (NLSE) in the 1+1 dimension by studying the dimensional reduction of
the self-dual Chern-Simons nonlinear Schr\"odinger model (NLSM) in the 2+1
dimension. It is found that this self-dual formulation allows us to find not
only the well-known soliton solutions from the Bogomol'nyi bound and the
Galilean boost, but also other soliton solutions in the presence of the
background sources.
