  We study the generation of dissipative solitons (DSs) in the model of the
fiber-laser cavities under the combined action of cubic-quintic nonlinearity,
multiphoton absorption and/or multiphoton emission (nonlinear gain) and gain
dispersion. A random component of the group-velocity dispersion (GVD) is
included too. The DS creation and propagation is studied by means of a
variational approximation and direct simulations, which are found to be in
reasonable agreement. With a proper choice of the gain, robust DS operation
regimes are predicted for different combinations of multiphoton absorption and
emission, in spite of the presence of the perturbation in the form of the
random GVD. Importantly, the zero background around the solitons remains stable
in the presence of the (necessary) linear gain. The solitons are stable too
against a certain (realistic) level of noise. Another essential finding is that
the quintic gain in the form of three-photon emission (3PE) offers an
alternative mechanism for supporting stable solitons, provided that it is not
too strong. The DSs coexist in low- and high amplitude forms, for a given value
of their width. The low-amplitude DS is stable, while its high-amplitude
counterpart is subject to the blowup instability, in the presence of the 3PE.
Interactions between DSs show various scenarios of the creation of breather
states through merger of the two solitons.
