  Corrections to the Thomas-Fermi-type solution of the Gross-Pitaevskii
equation are inevitable in order to get correctly the frequencies of the low
lying modes out of the Bogolyubov equations. These corrections are important in
the bulk, too, thus the failure of the Thomas-Fermi approximation is not
confined to the surface. We discuss this effect quantitatively and consider
similar phenomena of spin fluctuations in Bose-Einstein condensed gases in an
optical trap.
