  We present a dynamical description and analysis of non-equilibrium
transitions in the noisy one-dimensional Ginzburg-Landau equation for an
extensive system based on a weak noise canonical phase space formulation of the
Freidlin-Wentzel or Martin-Siggia-Rose methods. We derive propagating nonlinear
domain wall or soliton solutions of the resulting canonical field equations
with superimposed diffusive modes. The transition pathways are characterized by
the nucleations and subsequent propagation of domain walls. We discuss the
general switching scenario in terms of a dilute gas of propagating domain walls
and evaluate the Arrhenius factor in terms of the associated action. We find
excellent agreement with recent numerical optimization studies.
