Stability of solitary waves in random nonlocal nonlinear media

TL;DR

This paper demonstrates that nonlocality in nonlinear media significantly enhances the stability of bright solitons against random perturbations, with stability increasing as the noise correlation length approaches the soliton's size, supported by simulations and analytical estimates.

Contribution

It introduces a mean field approach to analytically estimate soliton stability and lifetime in nonlocal nonlinear media with correlated noise, advancing understanding of noise resilience.

Findings

Stability of solitons increases with noise correlation length.

Solitons are nearly insensitive to noise when correlation length matches soliton size.

Analytical estimates of soliton lifetime are derived for weakly correlated noise.

Abstract

We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schr\"odinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the nonlocality-induced finite correlation length of the noise in the transverse plane, by means of both numerical simulations and analytical estimates. In fact, solitons are practically insensitive to noise when the correlation length of the noise becomes comparable to the extent of the wave packet. We characterize soliton stability using two different criteria based on the evolution of the Hamiltonian of the soliton and its power. The first criterion allows us to estimate a time (or distance) over which the soliton preserves its form. The second criterion gives the life-time of the solitary wave packet in terms of its radiative power losses. We derive a simplified mean field approach which allows us to calculate the power loss analytically in the physically relevant case of weakly correlated noise, which in turn serves as a lower estimate of the life-time for correlated noise in general case.