# Modulational instability in nonlocal Kerr-type media with random parameters

## TL;DR

This paper investigates how nonlocality influences modulational instability in Kerr media with random parameters, showing that nonlocality can suppress or enhance instability depending on the response function's properties.

## Contribution

It provides an analytical and numerical study of the effects of nonlocality on stochastic modulational instability in Kerr media, highlighting the role of response function sign.

## Key findings

- Nonlocality suppresses growth rate peak and bandwidth of instability with sign-definite Fourier images.
- Nonlocality can enhance instability for response functions with negative-sign bands.
- Analytical and numerical methods confirm the contrasting effects of nonlocality.

## Abstract

Modulational instability of continuous waves in nonlocal focusing and defocusing Kerr media with stochastically varying diffraction (dispersion) and nonlinearity coefficients is studied both analytically and numerically. It is shown that nonlocality with the sign-definite Fourier images of the medium response functions suppresses considerably the growth rate peak and bandwidth of instability caused by stochasticity. Contrary, nonlocality can enhance modulational instability growth for a response function with negative-sign bands.