Dv. Skryabin et al., Perturbation theory for domain walls in the parametric Ginzburg-Landau equation - art. no. 056618, PHYS REV E, 6405(5), 2001, pp. 6618
We demonstrate that in the parametrically driven Ginzburg-Landau equation a
rbitrarily small nongradient corrections lead to qualitative differences in
the dynamical properties of domain walls in the vicinity of the transition
from rest to motion. These differences originate from singular rotation of
the eigenvector governing the transition. We present analytical results on
the stability of Ising walls, deriving explicit expressions for the critic
al eigenvalue responsible for the transition from rest to motion. We then d
evelop a weakly nonlinear theory to characterize the singular character of
the transition and analyze the dynamical effects of spatial inhomogeneities
.