Stability Analysis of Continuous Waves in Nonlocal Random Nonlinear Media

TL;DR

This paper investigates how nonlocality influences the stability of continuous waves in non-Kerr nonlinear media with randomness, revealing that nonlocality generally suppresses instability but can sometimes enhance it depending on response functions.

Contribution

It provides an analytical and numerical study of stability in nonlocal random nonlinear media, including higher-order moments and special response functions, which is novel.

Findings

Nonlocality suppresses growth rate peak and bandwidth of instability.

Certain response functions can cause nonlocality to enhance instability.

Higher-order moments are considered in the stability analysis.

Abstract

On the basis of the competing cubic-quintic nonlinearity model, stability (instability) of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the Gaussian white noise. It is shown that for different response functions of a medium nonlocality suppresses, as a rule, both the growth rate peak and bandwidth of instability caused by random parameters. At the same time, for a special form of the response functions there can be an ''anomalous'' subjection of nonlocality to the instability development which leads to further increase of the growth rate. Along with the second-order moments of the modulational amplitude, higher-order moments are taken into account.