Exact Bright and Dark Spatial Soliton Solutions in Saturable Nonlinear   Media
  We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schrodinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions. 
Gabriel F. Calvo, Juan Belmonte-Beitia, and Victor M. Perez-Garcia