  We propose a stability criterion of superfluids in condensed Bose-Einstein
systems, which incorporates the spectral function or the autocorrelation
function of the local density. Within the Gross-Pitaevskii-Bogoliubov theory,
we demonstrate the validity of our criterion for the soliton-emission
instability, with use of explicit forms of zero modes of the Bogoliubov
equation and a dynamical scaling near the saddle-node bifurcation. We also show
that the criterion is applicable to the Landau phonon instability and the
Landau roton instability within the single-mode approximation.
