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

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.