  Small quantum fluctuations in solitons described by the cubic-quintic
nonlinear Schr\"{o}dinger equation (CQNLSE) are studied with the linear
approximation. The cases of both self-defocusing and self-focusing quintic term
are considered (in the latter case, solitons may be effectively stable, despite
the possibility of collapse). The numerically implemented back-propagation
method is used to calculate the optimal squeezing ratio for the quantum
fluctuations vs. the propagation distance. In the case of the self-defocusing
quintic nonlinearity, opposite signs in front of the cubic and quintic terms
make the fluctuations around bistable pairs of solitons (which have different
energies for the same width) totally different. The fluctuations around
nonstationary Gaussian pulses in the CQNLSE model are studied too.
