  We study finite energy static solutions to a global symmetry breaking
Goldstone model described by an isovector scalar field in D+1 spacetime
dimensions. Both topologically stable multisolitons with arbitrary winding
numbers, and zero topological charge soliton--antisoliton solutions are
constructed numerically in D=3,4,5. We have explored the types of symmetries
the systems should be subjected to, for there to exist multisoliton and
soliton--antisoliton pairs in D=3,4,5,6. These findings are underpinned by
constructing numerical solutions in the $D\le 5$ examples. Subject to axial
symmetry, only multisolitons of all topological charges exist in even D, and in
odd D, only zero and unit topological charge solutions exist. Subjecting the
system to weaker than axial symmetries, results in the existence of all the
possibilities in all dimensions. Our findings apply also to finite 'energy'
solutions to Yang--Mills and Yang-Mills--Higgs systems, and in principle also
sigma models.
