A theorized object called a [geon][1], "an electromagnetic or gravitational wave which is held together in a confined region by the gravitational attraction of its own field energy", would seem like a match for what you're talking about. The wiki article mentions that exact solutions involving geons have been found, though it's not clear if they would be stable. For numerical simulations of various scenarios involving strong gravitational waves whose behavior is highly nonlinear, see [this pdf][2].


  [1]: http://en.wikipedia.org/wiki/Geon_(physics)
  [2]: http://cds.cern.ch/record/384064/files/9904013.pdf