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We obtain the well-known discrete modified Boussinesq equation intwo-component form as well as its Lax pair in $3\times3$ matrix form through a3-periodic reduction technique on the Hirota-Miwa equation and its Lax pair. Wedescribe how Darboux transformations and binary Darboux transformations can beconstructed for this two-component discrete integrable equation. Thesetransformations are then used to obtain classes of explicit solutions in theform of Casorati- and Gramm-type determinants. $N$-soliton solutions of thediscrete modified Boussinesq equation are discussed as well when taking thevacuum potentials as constants.

Binary Darboux transformations for discrete modified Boussinesq equation