We consider constant boundary conditions (cbc) for the Ablowitz-Kaup-Newell-Segur(AKNS) system in the framework of the sl(2) affine Kac-Moody algebra formulation. Through the dressing transformation and the tau function approach we obtain its soliton solutions and classify them according to their regular or singular behaviors. Moreover, by the analytic continuation method it is obtained the dark soliton solution of the well-known nonlinear Schrodinger equation (NLS) with cbc, which turns out to be a submodel of the AKNS system.Revisión por pares