the saddle ($\phi=\pi$) and the source ($\phi=0$). Any additional solutions should interpolate either between the two saddles or between the saddles and the sources. But the only directions from the two saddles which are not connected to another vacuum are those that point outwards. Therefore no soliton can exist that starts from one saddle to go to the other or from a saddle to go to a source. In fact, the outward directions from the saddles and some of the directions from the sources are connected to a sink at $$(\theta, \phi)=({\pi\over 2}, {\pi\over2})\ ,
\eqn\fournew$$ which is a fixed point of the flow described by the equations , $n=2$, but [*not*]{} a vacuum of the theory. We shall conjecture in the next section that a similar behaviour occurs in all $SU(2)$ models with $n$ even.

The SU(2) $n>2$ models
======================

The equations  or  for $SU(2)$ models with $n>2$ and $\kappa\not= 0$ are rather involved and we have not been able to find the solitons that lie in the complement of the maximal torus of $SU(2)$. Another way to proceed is to investigate the qualitative properties of the solutions of these equations by linearising them about the vacua of the 