  We analyze quasi-topological solitons winding around a mexican-hat potential
in two space-time dimensions.
  They are prototypes for a large number of physical excitations, including
Skyrmions of the Higgs sector of the standard electroweak model, magnetic
bubbles in thin ferromagnetic films, and strings in certain non-trivial
backgrounds.
  We present explicit solutions, derive the conditions for classical stability,
and show that contrary to the naive expectation these can be satisfied in the
weak-coupling limit. In this limit we can calculate the soliton properties
reliably, and estimate their lifetime semiclassically. We explain why gauge
interactions destabilize these solitons, unless the scalar sector is extended.
