Zero-crosstalk junctions made from dark solitons

The bound state solutions of the linear Schrodinger equation describing steady propagation of a signal in a planar waveguide are explicitly obtained for the case of a refractive index profile created by the interaction of N arbitrary dark solitons in a defocusing Kerr medium. Analysis of these solutions shows that linear signals confined to the arms of the waveguide prior to the collision do not interfere with each other at all as they pass through the interaction region of the dark solitons. Each signal emerges from the collision with exactly the same power and angle as it had at the input, thus behaving as though all solitons other than the one in which it was initially confined were altogether absent.