  We study the temporal evolution of a coherent state under the action of a
parametric oscillator and a nonlinear Kerr-like medium. We make use of the
interaction picture representation and use an exact time evolution operator for
the time independent part of the Hamiltonian. We approximate the interaction
picture Hamiltonian in such a way as to make it a member of a Lie algebra. The
corresponding time evolution operator behaves like a squeezing operator due to
the temporal dependence of the oscillator's frequency. We analyze the
probability amplitude and the auto correlation function for different
Hamiltonian parameters and we find a very good agreement between our
approximate results and converged numerical calculations.
