Influences of the interaction of the displaced-number-state field with
a Kerr medium on phase properties of the field are investigated. The
interaction brings about the symmetrical splitting of the phase probab
ility distribution (PPD) sometimes. Collapses and revivals have also b
een found in the long-time behaviours of the Hermitian, cosine and sin
e phase operators at high intensities. In terms of the PPD, the origin
for generating these revivals has been revealed.