Are rare rogue fluctuations generic to strongly nonlinear and non-integrable systems?

TL;DR

This paper investigates whether rare rogue fluctuations are common in strongly nonlinear, non-integrable systems, using extensive simulations of the $eta$-FPUT model, and finds they may indeed be a generic feature at late times.

Contribution

It demonstrates that rare rogue fluctuations are likely generic in non-integrable, strongly nonlinear systems, extending previous findings from granular chains to FPUT systems.

Findings

Rare RF may be common in non-integrable, strongly nonlinear systems.

RF are distinct from Peregrine solitons used in weakly nonlinear regimes.

Initial conditions and harmonic forces influence RF occurrence.

Abstract

Extensive dynamical simulations are used to explore the possible existence of sudden sufficiently large energy or rogue fluctuations (RF) at late times and across short time windows in the {\it strongly nonlinear regime} of the $\beta$-Fermi-Pasta-Ulam-Tsingou (FPUT) type systems. Our studies build on a study of RF in the non-dissipative granular chain system and suggest that {\it rare RF may be generic to non-integrable, strongly nonlinear systems at late enough times}. We comment on the role of initial conditions and the intriguing influence of harmonic forces on these strongly nonlinear systems. The RF under focus here are distinct from the well known Peregrine solitons used to describe rogue waves via the weakly nonlinear Schr\"odinger equation.