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 …