Two-Dimensional N=(2,2) Dilaton Supergravity from Graded Poisson-Sigma   Models II: Analytic Solution and BPS States
  The integrability of N=(2,2) dilaton supergravity in two dimensions is studied by the use of the graded Poisson Sigma model approach. Though important differences compared to the purely bosonic models are found, the general analytic solutions are obtained. The latter include minimally gauged models as well as an ungauged version. BPS solutions are an especially interesting subclass. 
L. Bergamin and W. Kummer