[en] We propose a soluble model to incorporate the nonlinear effects in the transition probabilities of the multiphonon Giant Dipole Resonances based on the SU(1,1) algebra. Analytical expressions for the multi-phonon transition probabilities are derived. For reasonably small magnitude of nonlinearity x ∼ 0.1 - 0.2 enhancement factor for the Double Giant Resonance excitation probabilities and the cross sections reaches values 1.3 - 2 compatible with experimental data. (author)