  We consider the dynamics of polarization of a single domain wall in a
magnetic nanowire, which is strongly pinned by impurities. In this case the
equation of motion for the polarization parameter does not include any other
dynamical variables and is nonlinear due to magnetic anisotropy. We calculated
numerically the magnetization dynamics for different choices of parameters
under short current pulses inducing polarization switching. Our results show
that the switching is most effective for very rapid current pulses. Damping
also enhances the switching probability.
