  We investigate the dynamics of matter-wave solitons in the presence of a
spatially varying atomic scattering length and nonlinearity. The dynamics of
bright and dark solitary waves is studied using the corresponding
Gross-Pitaevskii equation. The numerical results are shown to be in very good
agreement with the predictions of the effective equations of motion derived by
adiabatic perturbation theory. The spatially dependent nonlinearity leads to a
gravitational potential that allows to influence the motion of both fundamental
as well as higher order solitons.
