  In this paper, we continue the development of a generic adiabatic scheme for
nonlinear evolutions. We consider an abstract gradient flow of some energy
functional, together with a given manifold of static solutions arising from
broken symmetries. First, we list a number of explicit and generic conditions
on the energy functional that ensures the validity of our adiabatic scheme.
Then, we construct some explicit low-energy but no necessarily static
configurations, which form a stable manifold with finite codimensions for the
given gradient flow. Thirdly, we show that the gradient flow is globally
well-posed with initial configuration from the stable manifold. Finally, we
show that any solution to the full gradient flow starting from the stable
manifold is essentially governed by an effective equation on the manifold of
static solutions, up to a uniformly small and dissipating error term.
