  A model of two coupled Ablowitz-Ladik (AL) lattices is introduced. While the
system as a whole is not integrable, it admits reduction to the integrable AL
model for symmetric states. Stability and evolution of symmetric solitons are
studied in detail analytically (by means of a variational approximation) and
numerically. It is found that there exists a finite interval of positive values
of the coupling constant in which the symmetric soliton is stable, provided
that its mass is below a threshold value. Evolution of the unstable symmetric
soliton is further studied by means of direct simulations. It is found that the
unstable soliton breaks up and decays into radiation, or splits into two
counter-propagating asymmetric solitons, or evolves into an asymmetric pulse,
depending on the coupling coefficient and the mass of the initial soliton.
