A remark on the algebraic normal form method applied to the   Dirac-Klein-Gordon system in two space dimensions
  We consider the massive Dirac-Klein-Gordon system in two space dimensions. Under the non-resonace mass condition, we show that the solution is asymptotically free if the initial data are sufficiently small in a suitable weighted Sobolev space. In particular, it turns out that the Dirac component of the DKG system tends to a solution of the free Dirac equation. Our proof is based on the algebraic normal form method. 
Masahiro Ikeda, Akihiro Shimomura, Hideaki Sunagawa
math.AP