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We study interactions between bright matter-wave solitons which acquirechiral transport dynamics due to an optically-induced density-dependent gaugepotential. Through numerical simulations, we find that the collision dynamicsfeature several non-integrable phenomena, from inelastic collisions includingpopulation transfer and radiation losses to short-lived bound states andsoliton fission. An effective quasi-particle model for the interaction betweenthe solitons is derived by means of a variational approximation, whichdemonstrates that the inelastic nature of the collision arises from a couplingof the gauge field to velocities of the solitons. In addition, we derive a setof interaction potentials which show that the influence of the gauge fieldappears as a short-range potential, that can give rise to both attractive andrepulsive interactions.

Non-integrable dynamics of matter-wave solitons in a density-dependent gauge theory