  We present X-ray and optical data on the Be/X-ray binary (BeXRB) pulsar IGR
J01054-7253 = SXP11.5 in the Small Magellanic Cloud (SMC). Rossi X-ray Timing
Explorer (RXTE) observations of this source in a large X-ray outburst reveal an
11.483 +/- 0.002s pulse period and show both the accretion driven spin-up of
the neutron star and the motion of the neutron star around the companion
through Doppler shifting of the spin period. Model fits to these data suggest
an orbital period of 36.3 +/- 0.4d and Pdot of (4.7 +/- 0.3) x 10^{-10}
ss^{-1}. We present an orbital solution for this system, making it one of the
best described BeXRB systems in the SMC. The observed pulse period, spin-up and
X-ray luminosity of SXP11.5 in this outburst are found to agree with the
predictions of neutron star accretion theory. Timing analysis of the long-term
optical light curve reveals a periodicity of 36.70 +/- 0.03d, in agreement with
the orbital period found from the model fit to the X-ray data. Using blue-end
spectroscopic observations we determine the spectral type of the counterpart to
be O9.5-B0 IV-V. This luminosity class is supported by the observed V-band
magnitude. Using optical and near-infrared photometry and spectroscopy, we
study the circumstellar environment of the counterpart in the months after the
X-ray outburst.
