Numerical study of solitary waves in Dirac--Klein--Gordon system

Abstract: We use numerics to construct solitary waves in Dirac--Klein--Gordon (in one and three spatial dimensions) and study the dependence of energy and charge on $ω$. For the construction, we use the iterative procedure, starting from solitary waves of nonlinear Dirac equation, computing the corresponding scalar field, and adjusting the coupling constant. We also consider the case of massless scalar field, when the iteration procedure could be compared with the shooting method. We use the virial identities to control the error of simulations. We also discuss possible implications from the obtained results for the spectral stability of solitary waves.