A remark on asymptotic completeness for the critical nonlinear   Klein-Gordon equation
  We give a short proof of asymptotic completeness and global existence for the cubic Nonlinear Klein-Gordon equation in one dimension. Our approach to dealing with the long range behavior of the asymptotic solution is by reducing it, in hyperbolic coordinates to the study of an ODE. Similar arguments extend to higher dimensions and other long range type nonlinear problems. 
Hans Lindblad and Avy Soffer