  We consider the interplay of repulsive short-range and same-sign long-range
interactions in the dynamics of dark solitons, as prototypical coherent
nonlinear excitations in a trapped 1D Bose gas. First, the form of the ground
state is examined, and then both the existence of the solitary waves and their
stability properties are explored, and corroborated by direct numerical
simulations. We find that single- and multiple-dark-soliton states can exist
and are generically robust in the presence of long-range interactions. We
analyze the modes of vibration of such excitations and find that their
respective frequencies are significantly upshifted as the strength of the
long-range interactions is increased. Indeed, we find that a prefactor of the
long-range interactions considered comparable to the trap strength may upshift
the dark soliton oscillation frequency by {\it an order of magnitude}, in
comparison to the well established one of $\Omega/\sqrt{2}$ in a trap of
frequency $\Omega$.
