Brane solutions and integrability: a status report
  We review the status of the integrability and solvability of the geodesics equations of motion on symmetric coset spaces that appear as sigma models of supergravity theories when reduced over respectively the timelike and spacelike direction. Such geodesic curves describe respectively timelike and spacelike brane solutions. We emphasize the applications to black holes. 
W. Chemissany, P. Fr\'e, J. Rosseel, A. S. Sorin, M. Trigiante, and T.   Van Riet
hep-th