  We study the motion of solitary-wave solutions of a family of focusing
generalized nonlinear Schroedinger equations with a confining, slowly varying
external potential, $V(x)$. A Lyapunov-Schmidt decomposition of the solution
combined with energy estimates allows us to control the motion of the solitary
wave over a long, but finite, time interval. We show that the center of mass of
the solitary wave follows a trajectory close to that of a Newtonian point
particle in the external potential $V(x)$ over a long time interval.
