  We characterize the collective modes of a soliton train in a
quasi-one-dimensional Fermi superfluid, using a mean-field formalism. In
addition to the expected Goldstone and Higgs modes, we find novel long-lived
gapped modes associated with oscillations of the soliton cores. The soliton
train has an instability that depends strongly on the interaction strength and
the spacing of solitons. It can be stabilized by filling each soliton with an
unpaired fermion, thus forming a commensurate Fulde-Ferrell-Larkin-Ovchinnikov
(FFLO) phase. We find that such a state is always dynamically stable, which
paves the way for realizing long-lived FFLO states in experiments via phase
imprinting.
