Equivariant Schr\"odinger Maps in two spatial dimensions: the $\H^2$   target
  We consider equivariant solutions for the Schr\"odinger map problem from $\R^{2+1}$ to $\H^2$ with finite energy and show that they are global in time and scatter. 
Ioan Bejenaru, Alexandru Ionescu, Carlos E. Kenig, Daniel Tataru
math.AP