We present a comparative study of the non-linear wave packet dynamics of two-mode coherent
states of the Heisenberg-Weyl group, the SU(1,1) group and the SU(2) group under the action of
a model anharmonic Hamiltonian. In each case, we find certain generic signatures of non-linear
evolution such as quick onset of decoherence followed by Schrödinger cat formation
and revival. We also report important differences in the evolution of coherent states belonging
to different symmetry groups.
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