  In the present work, we examine the potential robustness of extreme wave
events associated with large amplitude fluctuations of the Peregrine soliton
type, upon departure from the integrable analogue of the discrete nonlinear
Schr\"odinger (DNLS) equation, namely the Ablowitz-Ladik (AL) model. Our model
of choice will be the so-called Salerno model, which interpolates between the
AL and the DNLS models. We find that rogue wave events essentially are
drastically distorted even for very slight perturbations of the homotopic
parameter connecting the two models off of the integrable limit. Our results
suggest that the Peregrine soliton structure is a rather sensitive feature of
the integrable limit, which may not persist under "generic" perturbations of
the limiting integrable case.
