On stabilization of small solutions in the nonlinear Dirac equation with   a trapping potential
  We consider a Dirac operator with short range potential and with eigenvalues. We add a nonlinear term and we show that the small standing waves of the corresponding nonlinear Dirac equation (NLD) are attractors for small solutions of the NLD. This extends to the NLD results already known for the Nonlinear Schr\"odinger Equation (NLS) 
Scipio Cuccagna, Mirko Tarulli
math.AP