Traveling dark solitons in superfluid Fermi gases

Families of dark solitons exist in superfluid Fermi gases. The energy-velocity dispersion and number of depleted particles completely determine the dynamics of dark solitons on a slowly varying background density. For the unitary Fermi gas, we determine these relations from general scaling arguments and conservation of local particle number. We find solitons to oscillate sinusoidally at the trap frequency reduced by a factor of 1/3. Numerical integration of the time-dependent Bogoliubov-de Gennes equation determines spatial profiles and soliton-dispersion relations across the BEC-BCS crossover, and proves consistent with the scaling relations at unitarity.