  We give a new proof of well posedness of the inverse modified scattering
problem for the Vlasov--Poisson system: for every suitable scattering profile
there exists a solution of Vlasov--Poisson which disperses and scatters, in a
modified sense, to this profile. Further, as a consequence of the proof, the
solutions are shown to admit a polyhomogeneous expansion, to any finite but
arbitrarily high order, with coefficients given explicitly in terms of the
scattering profile. The proof does not exploit the full ellipticity of the
Poisson equation.
