  The Hong-Ou-Mandel experiment leads indistinguishable photons simultaneously
reaching a 50:50 beam splitter to emerge on the same port through two-photon
interference. Motivated by this phenomenon, we consider numerical experiments
of the same flavor for classical, {\it wave} objects in the setting of
repulsive condensates. We examine dark solitons interacting with a repulsive
barrier, a case in which we find no significant asymmetries in the emerging
waves after the collision, presumably due to their topological nature. We also
consider case examples of two-component systems, where the dark solitons trap a
bright structure in the second-component (dark-bright solitary waves). For
these, pronounced asymmetries upon collision {\it are} possible for the
non-topological bright component. We also show an example of a similar
phenomenology for ring dark-bright structures in two dimensions.
