Uniqueness in the inverse scattering problem for Hartree type equation

Abstract

In this paper we consider the inverse scattering problem for the following Hartree type equation: \[ i\frac{\partial u}{\partial t} = -\varDelta u + (|x|^{-\sigma} * |u|^2) u. \] We prove the uniqueness theorem on the inverse scattering problem with respect to the power $\sigma$.