Asymptotic stability of solitary waves in generalized Gross--Neveu model

摘要: For the nonlinear Dirac equation in (1+1)D with scalar self-interaction (Gross--Neveu model), quintic and higher order nonlinearities (and within certain range of parameters), we prove that solitary wave solutions are asymptotically stable "even" subspace perturbations (to ignore translations eigenvalues $\pm 2\omega i$). The asymptotic stability is proved for initial data $H^1$. approach based on spectral information about linearization at waves which justify by numerical simulations. proof, develop theory linearized operators obtain appropriate estimates mixed Lebesgue spaces, without weights.