Solution Generation Methods II

We continue our discussion on the mathematical techniques which can be used for the construction of exact solutions of the five-dimensional stationary and axisymmetric Einstein equations in vacuum. We consider the complete integrability of the field equations and the inverse scattering method as a solution generation technique. The application of the inverse scattering method is discussed in detail focussing on the subtle and non-trivial steps. The procedure is demonstrated in practice for the systematic derivation of a range of black hole solutions. Finally we comment on the relation with the Bäcklund transformations and the equivalence of the two techniques for certain classes of solutions.