N-fold Darboux transformation and soliton solutions for a nonlinear Dirac system

From a spectral problem and corresponding Lenard operator pairs, we derive a Dirac soliton hierarchy associated with a nonlinear Dirac system. A systematic method is proposed for constructing the N-fold Darboux transformation of the Dirac system based on its Lax pair. As an application of Darboux transformation, explicit soliton solutions of the Dirac system are given.