Current and field driven domain wall motion under influence of the Dzyaloshinsky-Moriya interaction

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 $\varphi -q$ 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.