$S$ duality and exact type IIB superstring backgrounds

A geometrical approach in the nonsymmetric connection framework is employed to examine the issue of higher order ${\alpha }^{\prime }$ corrections to $D=10\mathrm{}$ type IIB superstring backgrounds with a covariantly constant null Killing isometry and nonzero Ramond-Ramond field content. These describe generalized supersymmetric string waves and were obtained recently by us through the $S$-duality transformations of purely NS-NS plane wave backgrounds. We find that the backgrounds are exact, subject to the existence of certain field redefinitions and provided certain restrictive conditions are satisfied.