Analytic study on soliton solutions for a Dirac integrable equation

Abstract Solitons are widely used in nonlinear optics, theoretical physics and other fields. In this paper, based on a spectral problem, the Dirac integrable equation is dealt with N-fold Darboux transformation, and analytic solutions for this equation are presented with the assistance of symbolic computation, and the propositions are provided for two different Darboux transformations. Two illustrative examples of the resulting solutions are displayed. Finally, their dynamic properties of those obtained solutions are discussed.