  We continue the study of solitons over noncommutative tori from the
perspective of time-frequency analysis and treat the case of a general
topological charge. Solutions are associated with vector bundles of higher rank
over noncommutative tori. We express these vector bundles in terms of
vector-valued Gabor frames and apply the duality theory of Gabor analysis to
show that Gaussians are solitons of general topological charge over
noncommutative tori. An energy functional for projections over noncommutative
tori is the basis for the self and anti-self duality equations of the solitons
which turns out to have a reformulation in terms of Gabor atoms and we prove
that projections generated by Gaussians minimize this energy functional.
Finally, we comment on the case of the Moyal plane and the associated
continuous vector-valued Gabor frames and show that Gaussians are the only
class of solitons.
