Interaction for Solitary Waves with a Phase Difference in a Nonlinear   Dirac Model
  This paper presents a further numerical study of the interaction dynamics for solitary waves in a nonlinear Dirac field with scalar self-interaction by using a fourth order accurate Runge-Kutta discontinuous Galerkin method. Our experiments are conducted on the Dirac solitary waves with a phase difference. Some interesting phenomena are observed: (a) full repulsion in binary and ternary collisions and its dependence on the distance between initial waves; (b) repulsing first, attracting afterwards, and then collapse in binary and ternary collisions of initially resting two-humped waves; (c) one-overlap interaction and two-overlap interaction in ternary collisions of initially resting waves. 
Sihong Shao, Huazhong Tang