  We report on continued monitoring of the Anomalous X-ray pulsar (AXP) 1E
1048.1-5937 using the Rossi X-ray Timing Explorer. We confirm that this pulsar
has exhibited significant pulsed flux variability. The principal features of
this variability are two pulsed X-ray flares. Both flares lasted several months
and had well-resolved few-week-long rises. The long rise times of the flares
are a phenomenon not previously reported for this class of object. The epochs
of the flare peaks were MJD 52,218.8+/-4.5 and 52,444.4+/-7.0. Both flares had
shorter rise than fall times. The flares had peak fluxes of 2.21+/-0.16 and
3.00+/-0.13 times the quiescent value. We estimate a total 2-10 keV energy
release of ~2.7x10^40 ergs and ~2.8x10^41 ergs for the flares, assuming a
distance of 5 kpc. We also report large (factor of ~12) changes to the pulsar's
spin-down rate on time scales of weeks to months, shorter than has been
reported previously. We find marginal evidence for correlation between the flux
and spin-down rate variability, with probability of nonrandom correlation 6%.
We discuss the implications of our findings for AXP models.

Astrophysics