  In this paper, classical small perturbations against a stationary solution of
the nonlinear Schrodinger equation with the general form of nonlinearity are
examined. It is shown that in order to obtain correct (in particular, conserved
over time) nonzero expressions for the basic integrals of motion of a
perturbation even in the quadratic order in the expansion parameter, it is
necessary to consider nonlinear equations of motion for the perturbations. It
is also shown that, despite the nonlinearity of the perturbations, the
additivity property is valid for the integrals of motion of different nonlinear
modes forming the perturbation (at least up to the second order in the
expansion parameter).
