Rare rogue fluctuations could be generic to strongly nonlinear and non-integrable systems

Abstract

We explore the possible existence of sufficiently large energy or rogue fluctuations (RFs) at late times in the strongly nonlinear regime of the classic $\beta$ Fermi–Pasta–Ulam–Tsingou (FPUT) type systems. Our studies build on a study of RFs in the non-dissipative granular chain system and suggest that rare RFs could be generic to the time evolution of non-integrable strongly nonlinear systems at late enough times. Given the nonlinearity and the nonintegrability, analytical studies are largely inaccessible. The studies have hence been carried out using extensive dynamical simulations. We comment on the role of initial conditions and the surprising influence of harmonic forces on these strongly nonlinear systems. The RFs under focus here are distinct from the well known Peregrine solitons used to describe rogue waves via the weakly nonlinear Schrödinger equation.