Extreme events in discrete nonlinear lattices

TL;DR

This paper investigates extreme wave events in discrete nonlinear lattices, revealing power law distributions and increased rogue wave probability near the integrable limit, linked to soliton interactions and stochasticity transitions.

Contribution

It introduces a statistical analysis of rogue waves in the Salerno model, connecting extreme event likelihood to soliton interactions and system integrability.

Findings

Power law distribution of wave amplitudes.

Enhanced rogue wave probability near integrable limit.

Transition from local to global stochasticity linked to soliton interactions.

Abstract

We perform statistical analysis on discrete nonlinear waves generated though modulational instability in the context of the Salerno model that interpolates between the intergable Ablowitz-Ladik (AL) equation and the nonintegrable discrete nonlinear Schrodinger (DNLS) equation. We focus on extreme events in the form of discrete rogue or freak waves that may arise as a result of rapid coalescence of discrete breathers or other nonlinear interaction processes. We find power law dependence in the wave amplitude distribution accompanied by an enhanced probability for freak events close to the integrable limit of the equation. A characteristic peak in the extreme event probability appears that is attributed to the onset of interaction of the discrete solitons of the AL equation and the accompanied transition from the local to the global stochasticity monitored through the positive Lyapunov exponent of a nonlinear map.