Rogue Fluctuations in Fermi-Pasta-Ulam-Tsingou Systems

Rogue waves, also referred to as freak waves, are large, short lived waves in the oceans and have been the subject of intense research due to their destructive nature. We consider discrete strongly nonlinear systems with Fermi-Pasta-Ulam-Tsingou type potentials by means of extensive simulations. We define rogue fluctuations in these systems as large and persistent kinetic energy fluctuations with finite lifetimes in these systems at late enough times. Our simulations suggest that rogue fluctuations are generic to strongly nonlinear systems. We also observe from our simulations that rogue fluctuations show features which are reminiscent of rogue waves in the oceans, providing evidence that they are natural candidates for analogs of rogue waves in discrete systems [1]. Effects arising from the presence of phonons in these systems are also explored.

[1] D. Han, M. Westley and S. Sen, Phys. Rev. E 90, 032904 (2014).