We consider certain boundary conditions supporting soliton solutions in the generalized nonlinear Schrödinger equation (AKNS r) (r = 1, 2). Using the dressing transformation (DT) method and the related tau functions, we study the AKNS r system for the vanishing, (constant) non-vanishing and the mixed boundary conditions, and their associated bright, dark and brightdark N-soliton solutions, respectively. Moreover, we introduce a modified DT related to the dressing group in order to consider the free-field boundary condition and derive generalized N darkdark solitons. As a reduced submodel of the AKNS r system, we study the properties of the focusing, defocusing and mixed focusingdefocusing versions of the so-called coupled nonlinear Schrödinger equation (r-CNLS), which has recently been considered in many physical applications. We have shown that two-darkdark-soliton bound states exist in the AKNS 2 system, and three- and higher-darkdark-soliton bound states cannot exist. The AKNS r (r 3) extension is briefly discussed in this approach. The properties and calculations of some matrix elements using level-one vertex operators are outlined. Dedicated to the memory of S S Costa © 2012 IOP Publishing Ltd.