  Toy models of interacting Pomerons with triple and quaternary Pomeron
vertices in zero transverse dimension are investigated. Numerical solutions for
eigenvalues and eigenfunctions of the corresponding Hamiltonians are obtained,
providing the quantum solution for the scattering amplitude in both models. The
equations of motion for the Lagrangians of the theories are also considered and
the classical solutions of the equations are found. Full two-point Green
functions ("effective" Pomeron propagator) and amplitude of diffractive
dissociation process are calculated in the framework of RFT-0 approach. The
importance of the loops contribution in the amplitude at different values of
the model parameters is discussed as well as the difference between the models
with and without quaternary Pomeron vertex.
