  We consider a problem of nonlinear response to an external electromagnetic
radiation of conventional disordered superconductors which contain a small
amount of weak magnetic impurities. We focus on the diffusive limit and use
Usadel equation to analyze the collective excitations and obtain the dispersion
relations for the collective modes. We determine the resonant frequency and
dispersion of both amplitude and phase (Carlson-Goldman) modes for moderate
strength of magnetic scattering. We find that the Carlson-Goldman and
superconducting plasmon modes can only be excited at some finite value of the
threshold momentum which increases with an increase in spin-flip scattering
rate while the amplitude mode is diffusive and becomes strongly suppressed with
the increase in spin-flip scattering. The value of the threshold momentum is
determined by the distance between the two consecutive spin-flip scattering
events. Furthermore, we also find that the superconducting plasmon mode becomes
gapless in the presence of the pair breaking processes. Possible ways towards
experimental verification of our results are also discussed.
