  Recent analytical and numerical work on field driven domain wall propagation
in nanowires has shown that for large transverse anisotropy and sufficiently
large applied fields the Walker profile becomes unstable before the breakdown
field, giving way to a slower stationary domain wall. We perform an asymptotic
expansion of the Landau Lifshitz Gilbert equation for large transverse magnetic
anisotropy and show that the asymptotic dynamics reproduces this behavior. At
low applied field the speed increases linearly with the field and the profile
is the classic Landau profile. Beyond a critical value of the applied field the
domain wall slows down. The appearance of a slower domain wall profile in the
asymptotic dynamics is due to a transition from a pushed to a pulled front of a
reaction diffusion equation.
