  For Lax-pair isospectral deformations whose associated spectrum, for given
initial data, consists of the disjoint union of a finitely denumerable discrete
spectrum (solitons) and a continuous spectrum (continuum), the matrix
Riemann-Hilbert problem approach is used to derive the leading-order
asymptotics as $| t | \to \infty$ $(x/t \sim \mathcal{O} (1))$ of solutions $(u
= u(x,t))$ to the Cauchy problem for the defocusing non-linear Schr\"{o}dinger
equation (D${}_{f}$NLSE), $\mi \partial_{t}u + \partial_{x}^{2}u - 2(| u |^{2}
- 1) u = 0$, with finite-density initial data $u(x,0) =_{x \to \pm \infty} \exp
(\tfrac{\mi (1 \mp 1) \theta}{2})(1 + o(1))$, $\theta \in [0,2\pi)$. The
D${}_{f}$NLSE dark soliton position shifts in the presence of the continuum are
also obtained.
