  We consider the initial-value problem for the cubic-quintic NLS \[
(i\partial_t+\Delta)\psi=\alpha_1 \psi-\alpha_{3}\vert \psi\vert^2
\psi+\alpha_5\vert \psi\vert^4 \psi \] in three spatial dimensions in the class
of solutions with $|\psi(x)|\to c >0$ as $|x|\to\infty$. Here $\alpha_1$,
$\alpha_3$, $\alpha_5$ and $c$ are such that $\psi(x)\equiv c$ is an
energetically stable equilibrium solution to this equation. Normalizing the
boundary condition to $\psi(x)\to 1$ as $|x|\to\infty$, we study the associated
initial-value problem for $u=\psi-1$ and prove a scattering result for small
initial data in a weighted Sobolev space.
