Complete integrability of two-coupled discrete modified Korteweg-de Vries equations

We report that two-coupled discrete modified Korteweg-de Vries equations (2-dmKdV) governed by nonlinear partial differential-difference equations are completely integrable. We derive Lax matrices for 2-dmKdV and also show that it admits a sequence of generalized (non-point) symmetries and polynomial conserved densities establishing its complete integrability. Also exact solutions of it expressible in terms of Hyperbolic and Jacobian elliptic functions have been derived.