We consider the dynamics of the 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.