Flat Currents and Solutions of the Green--Schwarz Superstring on AdS₅i×S⁵

We show that for the Green--Schwarz superstring on AdS₅i×S⁵, the Cartan 1-forms associated with the flat currents given by Bena, Polchinski and Roiban Phys. Rev. D 69(2004)046002 also satisfy equations of motion and the Virasoro constraint. Thus one can generate a series of classical solutions with a spectrum parameter from the existing one, and these solutions have the same infinite set of classically conserved quantities.