  We propose a time-dependent partial differential equation model to
investigate the dynamical behavior of the parity-time (PT) symmetric laser
during the nonlinear stage of its operation. This model incorporates physical
effects such as the refractive index distribution, dispersion, material loss,
nonlinear gain saturation and self-phase modulation. We show that when the loss
is weak, multiple stable steady states and time-periodic states of light exist
above the lasing threshold, rendering the laser multi-mode. However, when the
loss is strong, only a single stable steady state of broken PT symmetry exists
for a wide range of the gain amplitude, rendering the laser single-mode. These
results reveal the important role the loss plays in maintaining the single-mode
operation of PT lasers.
