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We apply the long-wavelength approximation to the low energy effective stringaction in the context of Hamilton-Jacobi theory. The Hamilton-Jacobi equationfor the effective string action is explicitly invariant under scale factorduality. We present the leading order, general solution of the Hamilton-Jacobiequation. The Hamilton-Jacobi approach yields a solution consistent with theLagrange formalism. The momentum constraints take an elegant, simple form.Furthermore this general solution reduces to the quasi-isotropic one, if theevolution of the gravitational field is neglected. Duality transformation forthe general solution is written as a coordinate transformation in an abstractfield space.Comment: TeX file, minor change

HAMILTON–JACOBI APPROACH TO PRE-BIG BANG COSMOLOGY AT LONG WAVELENGTHS