  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.
