  We consider the formalism of small-x effective action for reggeized gluons,
Gribov (Sov Phys JETP 26:414, 1968), Lipatov (Nucl Phys B 452:369, 1995; Phys
Rep 286:131, 1997; Subnucl Ser 49:131, 2013, Int J Mod Phys Conf Ser
39:1560082, 2015; Int J Mod Phys A 31(28/29):1645011, 2016; EPJ Web Conf
125:01010, 2016) and Lipatov et al. (Sov J Nucl Phys 23:338, 1976; Sov Phys
JETP 45:199, 1977; Sov J Nucl Phys 28:822, 1978), and, following to the
approach developed in Bondarenko et al. (Eur Phys J C 77(8):527, 2017, Eur Phys
J C 77(9):630, 2017), calculate the classical gluon field to NNLO precision
with fermion loops included. It is demonstrated, that the the self-consistency
of the equations of motion in each perturbatie order in the approach is
equivalent to the transversality conditions applied to the solutions of the
equations in the lower orders, that allows to construct the solutions with the
help of some recursive scheme. Applications of the obtained results are also
discussed.
