  We study soliton oscillations in a trapped superfluid Fermi gas across the
Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. We
derive an exact equation relating the phase jump across the soliton to its
energy, and hence obtain an expression for the soliton period. Our analytic
approach is supported by simulations of the time-dependent Bogoliubov-de Gennes
equations, which show that the period dramatically increases as the soliton
becomes shallower on the BCS side of the resonance. Finally, we propose an
experimental protocol to test our predictions.
