  The Salerno model constitutes an intriguing interpolation between the
integrable Ablowitz-Ladik (AL) model and the more standard (non-integrable)
discrete nonlinear Schr{\"o}dinger (DNLS) one. The competition of local on-site
nonlinearity and nonlinear dispersion governs the thermalization of this model.
Here, we investigate the statistical mechanics of the Salerno one-dimensional
lattice model in the nonintegrable case and illustrate the thermalization in
the Gibbs regime. As the parameter interpolating between the two limits (from
DNLS towards AL) is varied, the region in the space of initial energy and
norm-densities leading to thermalization expands. The thermalization in the
non-Gibbs regime heavily depends on the finite system size; we explore this
feature via direct numerical computations for different parametric regimes.
