The frustrated Brownian motion of nonlocal solitary waves

TL;DR

This paper studies how nonlocality affects the Brownian motion of solitary waves in disordered media, showing that increased nonlocality can significantly suppress wave-packet diffusion through analytical and numerical methods.

Contribution

It introduces a perturbational approach to quantify the impact of nonlocality on wave dynamics in disordered environments, applicable to various nonlocal models.

Findings

Nonlocality reduces Brownian motion of solitary waves.

Analytical predictions match numerical simulations.

Effect persists with non-paraxial effects included.

Abstract

We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the Brownian motion of self-trapped wave-packets. The result is valid for any kind of nonlocality and in the presence of non-paraxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equation