  The full set of stationary states of the mean field of a Bose-Einstein
condensate in the presence of a potential step or point-like impurity are
presented in closed analytic form. The nonlinear Schr\"odinger equation in one
dimension is taken as a model. The nonlinear analogs of the continuum of
stationary scattering states, as well as evanescent waves, are discussed. The
solutions include asymmetric soliton trains and other wavefunctions of novel
form, such as a pair of dark solitons bound by an impurity.
