We study the spectral stability of solitary wave solutions to the nonlinear Diracequation in one dimension. We focus on the Dirac equation with cubic nonlinearity, knownas the Soler model in (1+1) dimensions and also as the massive Gross-Neveu model.Presented numerical computations of the spectrum of linearization at a solitary wave showthat the solitary waves are spectrally stable. We corroborate our results by findingexplicit expressions for several of the eigenfunctions. Some of the analytic results holdfor the nonlinear Dirac equation with generic nonlinearity.
