  Nonlinear optical media of Kerr type are described by a particular version of
an anharmonic quantum harmonic oscillator. The dynamics of this system can be
described using the Moyal equations of motion, which correspond to a quantum
phase space representation of the Heisenberg equations of motion. For the Kerr
system we derive exact solutions of the Moyal equations for a complete set of
observables formed from the photon creation and annihilation operators. These
Moyal solutions incorporate the asymptotics of the classical limit in a simple
explicit form. An unusual feature of these solutions is that they exhibit
periodic singularities in the time variable. These singularities are removed by
the phase space averaging required to construct the expectation value for an
arbitrary initial state. Nevertheless, for strongly number-squeezed initial
states the effects of the singularity remain observable.
