  Using the Painleve analysis preceded by appropriate transformations of
nonlinear systems under investigation, we discover two new cases in which the
Pietrzyk-Kanattsikov-Bandelow vector short pulse equation must be integrable
due to the results of the Painleve test. Those cases are technologically
important because they correspond to the propagation of polarized ultra-short
light pulses in usual isotropic silica optical fibers.
