# Optical Random Riemann Waves in Integrable Turbulence

## TL;DR

This paper explores integrable turbulence in optical fibers, revealing that its initial development involves interacting random Riemann waves, with statistical properties explained through nonlinear geometric optics.

## Contribution

It introduces a dispersive-hydrodynamic framework for understanding the initial stage of integrable turbulence in optical fibers, highlighting the role of random Riemann waves.

## Key findings

- Development of IT divided into two stages, initial pre-breaking described by Riemann waves.
- Low-tailed wave intensity statistics explained by Riemann invariants.
- Stationary probability densities of Riemann invariants provide new statistical insights.

## Abstract

We examine integrable turbulence (IT) in the framework of the defocusing cubic one-dimensional nonlinear Schr\"{o}dinger equation. This is done theoretically and experimentally, by realizing an optical fiber experiment in which the defocusing Kerr nonlinearity strongly dominates linear dispersive effects. Using a dispersive-hydrodynamic approach, we show that the development of IT can be divided into two distinct stages, the initial, pre-breaking stage being described by a system of interacting random Riemann waves. We explain the low-tailed statistics of the wave intensity in IT and show that the Riemann invariants of the asymptotic nonlinear geometric optics system represent the observable quantities that provide new insight into statistical features of the initial stage of the IT development by exhibiting stationary probability density functions.