  We apply the long-wavelength approximation to the low energy effective string
action in the context of Hamilton-Jacobi theory. The Hamilton-Jacobi equation
for the effective string action is explicitly invariant under scale factor
duality. We present the leading order, general solution of the Hamilton-Jacobi
equation. The Hamilton-Jacobi approach yields a solution consistent with the
Lagrange formalism. The momentum constraints take an elegant, simple form.
Furthermore this general solution reduces to the quasi-isotropic one, if the
evolution of the gravitational field is neglected. Duality transformation for
the general solution is written as a coordinate transformation in an abstract
field space.
