  A complete analytical description of the dynamics of current and field driven
transverse domain walls under the influence of the Dzyaloshinsky-Moriya
interaction using the $\phi - q$ model will be given. Five different scenarios
will be observed where the Dzyaloshinsky-Moriya vector is either parallel or
perpendicular to the easy axis anisotropy of the system and a direct reversal
respectively precessional motion will be assumed.

Mesoscale and Nanoscale Physics