  Effective field theory of BFKL pomerons interacting by QCD triple pomeron
vertices is investigated. Classical equations of motion for the effective
pomeron fields are presented being a minimal extension of the
Balitsky-Kovchegov equation that incorporates both merging and splitting of the
pomerons and that is self-dual. The equations are solved for symmetric boundary
conditions. The solutions provide the dominant contribution to the scattering
amplitudes in the semi-classical approximation. We find that for rapidities of
the scattering larger than a critical value Y_c at least two classical
solutions exist. Curiously, for each of the two classical solutions with the
lowest action the symmetry between the projectile and the target is found to be
spontaneously broken, being however preserved for the complete set of classical
solutions. The solving configurations at rapidities Y>Y_c consist of a Gribov
field being strongly suppressed even at very large gluon momenta and the
complementary Gribov field that converges at high Y to a solution of
Balitsky-Kovchegov equation. Interpretation of the results is given and
possible consequences are shortly discussed.
