Elliptic solutions in the Neumann–Rosochatius system with mixed flux

Closed strings spinning in AdS_3 x S^3 x T^4 with mixed Ramond-Ramond and Neveu-Schwarz-NeveuSchwarz three-form fluxes are described by a deformation of the one-dimensional Neumann-Rosochatius integrable system. In this articlewe find general solutions to this systemthat can be expressed in terms of elliptic functions. We consider closed strings rotating either in S^3 with two different angularmomenta or in AdS_3 with one spin. To find the solutions, we will need to extend the Uhlenbeck integrals of motion of the Neumann-Rosochatius system to include the contribution from the flux. In the limit of pure Neveu-Schwarz-NeveuSchwarz flux, where the problem can be described by a supersymmetricWess-Zumino-Witten model, we find exact expressions for the classical energy in terms of the spin and the angular momenta of the spinning string.