Do shape invariant solitons in highly nonlocal nematic liquid crystals really exist?

TL;DR

This paper investigates whether shape invariant solitons can physically exist in three-dimensional highly nonlocal nematic liquid crystals, finding that noise destabilizes them, making them practically unobservable.

Contribution

It uses a modified Petviashvili's method to find and analyze the stability of shape invariant solitons in realistic models of nematic liquid crystals.

Findings

Shape invariant solitons are theoretically found but are unstable under noise.

Added noise causes solitons to breathe, preventing their stable observation.

The solutions are not practically observable due to instability.

Abstract

We question physical existence of shape invariant solitons in three dimensional nematic liquid crystals. Using modified Petviashvili's method for finding eigenvalues and eigenfunctions, we determine shape invariant solitons in a realistic physical model that includes the highly nonlocal nature of the liquid crystal system. We check the stability of such solutions by propagating them for long distances. We establish that any noise added to the medium or to the fundamental solitons induces them to breathe, rendering them practically unobservable.