  We examine the variability of the high-ionization Lyman alpha lambda 1216
broad emission line (BEL) in a sample of 61 high-luminosity, high-redshift
quasars observed at two epochs by the Sloan Digital Sky Survey. These bright
objects lie in the redshift interval z=[2.5, 4.3] and have luminosities $3.4
\times 10^{45} \lesssim \lambda L_{\lambda} \lesssim 3.4 \times 10^{46}$ erg/s
at 1450A. Utilizing improved spectrophotometric flux calibrations relative to
nearby compact stars observed simultaneously, we are able to measure the flux
changes in Lyman alpha and the nearby continuum at two epochs. We find 20
objects that exhibit Lyman alpha BEL flux variability at a significance level
greater than 5 sigma on time-scales ranging from days to years in the quasar
rest frame. The results show that, although some earlier work showed no
significant detections of Lyman alpha BEL flux changes in a quasar sample with
even higher luminosity, variability is present and readily observable in the
sample studied here. We also consider the CIV lambda1549 BEL. The lack of a
strong correlation between Lyman alpha BEL variability and nearby continuum
variability is consistent with the presence of a time lag between the
variations, whereas the presence of a stronger correlation between Lyman alpha
BEL variability and CIV BEL variability suggests that these BEL regions (BELRs)
are at similar distances from the central ionizing source. Some interesting
examples are high-lighted in the analysis, including a case where the flux of
an Lyman alpha BEL increased by ~26% in 14 days in the quasar rest frame,
suggesting that the BELR has the shape of a disc, which is being observed
face-on. This work demonstrates that future campaigns of spectrophotometric
monitoring can improve our understanding of the structure of the BELRs of
high-luminosity, high-redshift quasars.
