  Kinetic energy driven phase transitions in Bose superfluids occur at low
values of the repulsion when the values of the next-to-nearest and
next-to-next-to-nearest hopping term attain certain critical values, resulting
in alterations in the wave vector of the condensate. We map out the space of
possible phases allowed by particular forms of the single-particle energy
dispersion in the superfluid state, noting the appearance of a new phase, and
examine in more detail the effects of additional repulsive terms on the form of
the condensate wavefunction. We also examine the effect of these additional
hopping terms on the formation of inhomogeneities in the condensate.
