  We consider a class of $1D$ NLS perturbed with a steplike potential. We prove
that the nonlinear solutions satisfy the double scattering channels in the
energy space. The proof is based on concentration-compactness/rigidity method.
We prove moreover that in dimension higher than one, classical scattering holds
if the potential is periodic in all but one dimension and is steplike and
repulsive in the remaining one.
