  The Ablowitz-Ladik chain is an integrable discretized version of the
nonlinear Schr\"{o}dinger equation. We report on a novel underlying Hamiltonian
particle system with properties similar to the ones known for the classical
Toda chain and Calogero fluid with $1/\sinh^2$ pair interaction. Boundary
conditions are imposed such that, both in the distant past and future,
particles have a constant velocity. We establish the many-particle scattering
for the Ablowitz-Ladik chain and obtain properties known for generic integrable
many-body systems. For a specific choice of the chain, real initial data remain
real in the course of time. Then, asymptotically, particles move in pairs with
a velocity-dependent size and scattering shifts are governed by the fusion
rule.
