Long range scattering for higher order Schrödinger operators

This paper is concerned with the scattering problem for the higher order Schrödinger operator (−Δ)m+V(x), where V(x) is a long-range potential. At this moment the classical wave operators do not exist, so we provide one kind of modified wave operators and show the existence and the asymptotic completeness of such wave operators, as well as the expression of the corresponding scattering operator.