  We study an ultracold atomic gas with attractive interactions in a
one-dimensional optical lattice. We find that its excitation spectrum displays
a quantum soliton band, corresponding to $N$-particle bound states, and a
continuum band of other, mostly extended, states. For a system of a finite
size, the two branches are degenerate in energy for weak interactions, while a
gap opens above a threshold value for the interaction strength. We find that
the interplay between degenerate extended and bound states has important
consequences for both static and dynamical properties of the system. In
particular, the solitonic states turn out to be protected from spatial
perturbations and random disorder. We discuss how such dynamics implies that
our system effectively provides an example of a quantum many-body system that,
with the variation of the bosonic lattice filling, crosses over from integrable
non-ergodic to non-integrable ergodic dynamics, through non-integrable
non-ergodic regimes.
