  We study the dynamics of localized pulses in the complex cubic-quintic
Ginzburg-Landau (GL) equation with strong nonlinearity management. The
generalized complex GL equation, averaged over rapid modulations of the
nonlinearity, is derived. We employ the variational approach to this averaged
equation to derive a dynamical system for the dissipative soliton parameters.
By using numerical simulations of this dynamical system and the full GP
equation, we show that nonlinearity-managed dissipative solitons exist in the
model. The parameter regions for stabilization of exploding soliton are
obtained.
