  The Hamilton-Jacobi equation for the string cosmology is solved using the
gradient expansion method. The zeroth order solution is taken to be the
standard pre-big bang model and the second order solution is found for the
dilaton and the three-metric. It indicates that corrections generated by
inhomogeneities of the seed metric are suppressed near the singularity and are
growing towards the asymptotic past, but corrections generated by the dilaton
inhomogeneities are growing near the singularity and are suppressed in the
past. Possible influences of initial metric inhomogeneities on the pre-big bang
superinflation are discussed.
