Abstract: By using Darboux transformation method, we discussed a class of discrete integrable systems. Starting from a new initial solution, the exact solutions of the equation were given by using Darboux transformation, and then the 1-bell-shaped soliton solution, 1-kink-shaped soliton solution, 2-anti-bell-shaped soliton solution and periodic solutions of the equation were given by choosing the appropriate parameters, and the images of these solutions were given. We analyzed their structures, elastic and inelastic collisions of these solutions through these images.

Key words: discrete integrable system, Darboux transformation method, soliton solution