Existence of localised solutions of (1+1)-dimensional nonlinear Dirac equations with scalar self-interaction

Abstract

Necessary and sufficient conditions for the existence of localised solutions of the form psi (x,t)=exp(-i omega t) phi (x), with phi real, of the classical equations of motion for (1+1)-dimensional nonlinear spinor field are presented. Furthermore, the authors give existence conditions for non-linear second-order equations obtained as a Klein-Gordon limit of the considered spinor field equations.