  In this report we demonstrate a simple model for the motion of a vortex
domain wall in a ferromagnetic strip of submicron width under the influence of
an external magnetic field. The model exhibits three distinct dynamical
regimes. In a viscous regime at low fields the wall moves rigidly with a
velocity proportional to the field. Above a critical field the motion becomes
underdamped as the vortex moves periodically across the strip; these
oscillations are accompanied by a slow drift with a decreasing velocity. At
still higher fields the drift velocity starts rising linearly with the field
again but with a much lower mobility dv/dH than in the low-field regime. We
calculate the relevant quantities and compare them to experimentally observed
values.
