  In this work dark soliton collisions in a one-dimensional superfluid Fermi
gas are studied across the BEC-BCS crossover by means of a recently developed
finite-temperature effective field theory [S. N. Klimin, J. Tempere, G.
Lombardi, J. T. Devreese, Eur. Phys. J. B 88, 122 (2015)] . The evolution of
two counter-propagating solitons is simulated numerically based on the theory's
nonlinear equation of motion for the pair field. The resulting collisions are
observed to introduce a spatial shift into the trajectories of the solitons.
The magnitude of this shift is calculated and studied in different conditions
of temperature and spin-imbalance. When moving away from the BEC-regime, the
collisions are found to become inelastic, emitting the lost energy in the form
of small-amplitude density oscillations. This inelasticity is quantified and
its behavior analyzed and compared to the results of other works. The
dispersion relation of the density oscillations is calculated and is
demonstrated to show a good agreement with the spectrum of collective
excitations of the superfluid.
