  We construct a three-dimensional analytically soluble model of the nonlinear
effects in Coulomb excitation of multiphonon Giant Dipole Resonances (GDR)
based on the SU(2,1) algebra. The full 3-dimensional model predicts further
enhancement of the Double GDR (DGDR) cross sections at high bombarding
energies. Enhancement factors for DGDR measured in thirteen different processes
with various projectiles and targets at different bombarding energies are well
reproduced with the same value of the nonlinearity parameter with the exception
of the anomalous case of $^{136}$Xe which requires a larger value.
