(Be sure to download -- the equations don't appear right in google docs "view" mode!)
OOps: 3/14/21023: in the 3D version, which is what really counts,
I can easily prove that the system is always unstable. Yes, even with
a definite topological charge for all physically realistic states, and with distinct subsets of the set of states for different topological charges ... there is never a state of minimum energy within the set!
Given that those conditions are the main arguments used in the paper of Erick Weinberg
to suggest that the solitons in the usual Georgi-Glashow-Thooft-Polyakov system are stable..
it is quite a shocker to realize this. Topology is not the guarantee it has been made out to be.
The question of stability of topological solitons, with topology based on a Higgs term, is
more serious than I thought....