Extreme events in near integrable lattices

TL;DR

This study investigates how extreme wave events, like rogue waves, are affected when moving away from an ideal integrable model, revealing their high sensitivity to small perturbations in near-integrable lattices.

Contribution

The paper demonstrates that rogue wave structures are highly sensitive and tend to distort under slight deviations from the integrable Ablowitz-Ladik model, highlighting their fragile nature.

Findings

Rogue wave events are drastically distorted with small perturbations.

Peregrine soliton structures are sensitive to deviations from integrability.

Extreme events do not persist under generic perturbations.

Abstract

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.