  We extend the Ginzburg-Landau (GL) theory of atomically rough bcc-liquid
interfaces [Wu {\it et al.}, Phys. Rev. B \textbf{73}, 094101 (2006)] outside
of equilibrium. We use this extension to derive an analytical expression for
the kinetic coefficient, which is the proportionality constant $\mu(\hat n)$
between the interface velocity along a direction $\hat n$ normal to the
interface and the interface undercooling. The kinetic coefficient is expressed
as a spatial integral along the normal direction of a sum of gradient square
terms corresponding to different nonlinear density wave profiles. Anisotropy
arises naturally from the dependence of those profiles on the angles between
the principal reciprocal lattice vectors $\vec K_i$ and $\hat n$. Values of the
kinetic coefficient for the$(100)$, $(110)$ and $(111)$ interfaces are compared
quantitatively to the prediction of linear Mikheev-Chernov (MC) theory [J.
Cryst. Growth \textbf{112}, 591 (1991)] and previous molecular dynamics (MD)
simulation studies of crystallization kinetics for a classical model of Fe.
Additional MD simulations are carried out here to compute the relaxation time
of density waves in the liquid in order to make this comparison free of fit
parameter. The GL theory predicts a similar expression for $\mu$ as the MC
theory but yields a better agreement with MD simulations for both its magnitude
and anisotropy due to a fully nonlinear description of density wave profiles
across the solid-liquid interface. GL theory is also used to derive an inverse
relation between $\mu$ and the solid-liquid interfacial free-energy. The
general methodology used here to derive an expression for $\mu(\hat n)$ also
applies to amplitude equations derived from the phase-field-crystal model,
which only differ from GL theory by the choice of cubic and higher order
nonlinearities in the free-energy density.
