N-fold Darboux transformation and discrete soliton solutions for the discrete Hirota equation

In this paper, a discrete Hirota equation is analytically investigated. The N-fold Darboux transformation (DT) is constructed based on the Lax pair for the equation. In addition, the discrete N-soliton solutions under the vanishing background are derived. Especially, the dynamic features of one-soliton and two-soliton solutions are displayed through figures.