  Dynamics of solitons of the Ablowitz-Ladik model in the presence of a random
potential is studied. In absence of the random potential it is an integrable
model and the solitons are stable. As a result of the random potential this
stability is destroyed. In some regime, for short times particle-like dynamics
with constant mass is found. There is another regime, where particle-like
dynamics with varying mass takes place. In particular an effective potential is
found. It predicts correctly changes in the direction of motion of the soliton.
This potential is a scaling function of time and strength of the potential,
leading to a relation between the first time when the soliton changes direction
and the strength of the random potential.
