Discrete modified Boussinesq equation and Darboux transformation

In this letter, by a 3-periodic reduction technique, we regain the well-known discrete modified Boussinesq equation and its Lax pairs. It is the first time that the Darboux transformation is successfully constructed for this discrete equation. We then obtain its explicit solutions in terms of Casoratian determinants. The derived solutions are soliton solutions when the seed solutions are taken as v=1 and w=1.