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

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