Rogue Waves, Self-similarity, and Integrable Turbulence

TL;DR

This paper investigates the emergence of rogue waves in integrable turbulence with self-similar behavior, demonstrating their universal occurrence as giant fluctuations through numerical simulations.

Contribution

It introduces a universal scenario for rogue wave formation in self-similar integrable turbulence, supported by numerical evidence across different source models.

Findings

Rogue waves are giant fluctuations away from self-similar dynamics.

The scenario is universal across various source correlation models.

Numerical simulations confirm the proposed mechanism.

Abstract

We explore extreme event occurrence in the integrable turbulence with self-similar asymptotics. We posit that rogue waves in such systems manifest themselves as giant fluctuations away from average self-similar dynamics of the system. We support our proposition with numerical simulations of rogue wave excitation in the self-similar regime of stimulated Raman scattering. We show that our results hold irrespective of a specific source correlation model, suggesting the universality of the proposed scenario.