  We develop a systematic asymptotic description for domain wall motion in
one-dimensional magnetic nanowires under the influence of small applied
magnetic fields and currents and small material anisotropy. The magnetization
dynamics, as governed by the Landau--Lifshitz--Gilbert equation, is
investigated via a perturbation expansion. We compute leading-order behaviour,
propagation velocities, and first-order corrections of both travelling waves
and oscillatory solutions, and find bifurcations between these two types of
solutions. This treatment provides a sound mathematical foundation for numerous
results in the literature obtained through more ad hoc arguments.
