  In the present work, we theoretically propose and numerically illustrate a
mean-field analogue of the Hong-Ou-Mandel experiment with bright solitons. More
specifically, we scatter two solitons off of each other (in our setup, the
bright solitons play the role of a classical analogue to the quantum photons of
the original experiment), while the role of the beam splitter is played by a
repulsive Gaussian barrier. In our classical scenario, distinguishability of
the particles yields, as expected, a $0.5$ split mass on either side.
Nevertheless, for very slight deviations from the completely symmetric scenario
a near-perfect transmission i.e., a $|2,0>e$ or a $|0,2 >$ state can be
constructed instead, very similarly to the quantum mechanical output. We
demonstrate this as a generic feature under slight variations of the relative
soliton speed, or of the relative amplitude in a wide parametric regime. We
also explore how variations of the properties of the "beam splitter" (i.e., the
Gaussian barrier) affect this phenomenology.
