  We present a mean-field theory numerical study of Tkachenko waves of a vortex
lattice in trapped atomic Bose-Einstein condenstates. Our results show
remarkable qualitative and quantitative agreement with recent experiments at
JILA. We extend our calculations beyond the conditions of the experiment,
probing deeper into the incompressible regime where we find excellent agreement
with analytical results. In addition, bulk excitations observed in the
experiment are discussed.
