Giant Resonances in Coulomb Excitations of Relativistic Ions

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 $x\simeq 0.1-0.2$ enhancement factor for the Double Giant Resonance excitation probabilities and the cross sections %in relativistic ion collisions reaches values $1.3-2$ compatible with experimental data.