  STU supergravity becomes an integrable system for solutions that effectively
only depend on two variables. This class of solutions includes the Kerr
solution and its charged generalizations that have been studied in the
literature. We here present an inverse scattering method that allows to
systematically construct solutions of this integrable system. The method is
similar to the one of Belinski and Zakharov for pure gravity but uses a
different linear system due to Breitenlohner and Maison and here requires some
technical modifications. We illustrate this method by constructing a
four-charge rotating solution from flat space. A generalization to other
set-ups is also discussed.
