Diffractive Nonlinear Geometrical Optics for Variational Wave Equations   and the Einstein Equations
  We derive an asymptotic solution of the vacuum Einstein equations that describes the propagation and diffraction of a localized, large-amplitude, rapidly-varying gravitational wave. We compare and contrast the resulting theory of strongly nonlinear geometrical optics for the Einstein equations with nonlinear geometrical optics theories for variational wave equations. 
Giuseppe Ali and John K. Hunter