  The Regge behaviour of the scattering amplitudes in perturbative QCD is
governed in the generalized leading logarithmic approximation by the
contribution of the color--singlet compound states of Reggeized gluons. The
interaction between Reggeons is described by the effective hamiltonian, which
in the multi--color limit turns out to be identical to the hamiltonian of the
completely integrable one--dimensional XXX Heisenberg magnet of noncompact spin
$s=0$. The spectrum of the color singlet Reggeon compound states - perturbative
Pomerons and Odderons, is expressed by means of the Bethe Ansatz in terms of
the fundamental $Q-$function, which satisfies the Baxter equation for the XXX
Heisenberg magnet. The exact solution of the Baxter equation is known only in
the simplest case of the compound state of two Reggeons, the BFKL Pomeron. For
higher Reggeon states the method is developed which allows to find its general
solution as an asymptotic series in powers of the inverse conformal weight of
the Reggeon states. The quantization conditions for the conserved charges for
interacting Reggeons are established and an agreement with the results of
numerical solutions is observed. The asymptotic approximation of the energy of
the Reggeon states is defined based on the properties of the asymptotic series,
and the intercept of the three--Reggeon states, perturbative Odderon, is
estimated.
