Perturbation theory for domain walls in the parametric Ginzburg-Landau equation - art. no. 056618

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 .