Exactly solvable boson model with cubic nonlinearity

The model of phase matched parametric amplifier, Hamiltonian of which has a cubic nonlinearity with respect to the Bose-field, is assumed. Exact operator solution is obtained. Evolution of the photon intensity and the corresponding variance is examined Conditions, defining the sub-Poissonian charachter of the number destribution and the squeezing of quantum fluctuations of modequadraturs, are obtained.