\phi')-a(\theta, \phi)$ while for the $SO(2)$ solitons $Q_T=Q$. Therefore the value of the topological charge of the $SO(2)$ solitons and the value of the topological charge of their embeddings as $SU(2)$ solitons are different. Apart from the $SU(2)$ solitons that lie on the maximal torus and we have examined above, the $SU(2)$ model has other solitons that interpolate between different vacua but otherwise lie entirely outside the maximal torus of $SU(2)$. We shall investigate these solitons in the following three sections.

The $SU(2)$ n=1 model
=====================

As we have seen in the previous section, there are static solitons that interpolate between the two vacua of $SU(2)$ $n=1$ model with $0\leq \kappa<1$ and lie entirely on the maximal torus of $SU(2)$. Here, we shall find another class of solitons for this model that interpolate between the two vacua but otherwise lie in the [*complement*]{} of the maximal torus of $SU(2)$. The equations  for $M,N$ in the $n=1$ case are $$\eqalign{
{d\over dx}M\pm m [-\kappa N+(1-M^2)]&=0
\cr
{d\over dx}N\pm m[\kappa M-NM]&=0
\ .}
\eqn\fived$$ Following \[\], we can find a class of solitons by setting $N=\kappa$. These solutions are $$\eqalign{
M&=\sqrt{1-\kappa^2} \tanh\big(\mp m \sqrt{1-\kappa^2}(x-x_0)\big)
\cr
N&=\kappa
\cr
U&=\sqrt{1-\kappa^2} \cosh^{-1}\big( m \sqrt{1-\kappa^2}(x-x_0)\big) \cos\psi
