Study of instability of the Fourier split-step method for the massive Gross–Neveu model

摘要: Abstract Stability properties of the well-known Fourier split-step method used to simulate a soliton and similar solutions nonlinear Dirac equations, known as Gross–Neveu model, are studied numerically analytically. Three distinct types numerical instability that can occur in this case, revealed explained. While one these be viewed being related occurring simulations Schrodinger equation, other two have not been or identified before, best our knowledge. These unconditional, i.e. for arbitrarily small values time step. They also persist continuum limit, fine spatial discretization. Moreover, them persists limit an infinitely large computational domain. It is further demonstrated instabilities methods applied soliton, well certain solitons another relativistic field theory massive Thirring.