Inverse modified scattering and polyhomogeneous expansions for the Vlasov–Poisson system

Abstract We give a new proof of well posedness of the inverse modified scattering problem for the Vlasov–Poisson system in three space dimensions: for every suitable scattering profile, describing an isolated system, 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.