Numerical study of solitary wave stability in cubic nonlinear Dirac equations in 1D

Recently there has occurred a controversy between the semi-analytical prediction of linear stability of the soliton of the massive Gross-Neveu model and direct numerical observations of its instability for small values of the frequency. We revisit the problem of numerical computation of this soliton, find a mechanism behind the numerical instability observed in earlier studies, and propose methods to stably compute the soliton over long times. Thus, we confirm the semi-analytical prediction of the soliton's being linearly stable.