  It was recently shown [V.V. Cherny, T. Byrnes, A.N. Pyrkov, \textit{Adv.
Quantum Technol.} \textbf{2019} \textit{2}, 1800087] that the nonlinear
Schrodinger equation with a simplified dissipative perturbation of special kind
features a zero-velocity solitonic solution of non-zero amplitude which can be
used in analogy to attractors of Hopfield's associative memory. In this work,
we consider a more complex dissipative perturbation adding the effect of
two-photon absorption and the quintic gain/loss effects that yields formally
the complex Ginzburg-Landau equation (CGLE). We construct a perturbation theory
for the CGLE with a small dissipative perturbation and define the behavior of
the solitonic solutions with parameters of the system and compare the solution
with numerical simulations of the CGLE. We show that similarly to the nonlinear
Schrodinger equation with a simplified dissipation term, a zero-velocity
solitonic solution of non-zero amplitude appears as an attractor for the CGLE.
In this case the amplitude and velocity of the solitonic fixed point attractor
does not depend on the quintic gain/loss effects. Furthermore, the effect of
two-photon absorption leads to an increase in the strength of the solitonic
fixed point attractor.
