\cr
W&=\sqrt{1-\kappa^2} \cosh^{-1}\big( m \sqrt{1-\kappa^2}(x-x_0)\big) \sin\psi
\ ,}
\eqn\eightd$$ where $x_0, \psi$ are the modular parameters of the solution, $\cot\psi=\lambda$. It is clear that these solitons lie in the complement of the maximal torus since $U$ and $W$ do not vanish for any value of $x$ unless $x$ goes to infinity. The topology of the moduli space is $S^1\times \bR$: The modular parameter $x_0$ is due to the translational invariance of the underlying theory while the modular angular parameter $\psi$ is due to the charge $Q$ given in . These are reminiscent to the modular parameters of BPS monopoles in four-dimensions (see for example \[\]).

However, there is a more general class of $SU(2)$ solutions for which $N\not=\kappa$. To find these new solitons, we use the angular parameterisation and the equations   for $n=1$ become $$\eqalign{
{d\over dx}\theta&=\pm m[-\kappa \cos \phi+\sin(\theta)]
\cr
{d\over dx}\phi&=\pm m\kappa \cot\theta \sin\phi\ .}
\eqn\ninedaa$$ As it can been seen from , the $SU(2)$ $n=1$ model has two vacua $(\theta_0, 0)$ and $(\pi-\theta_0, 0)$. We remark that a linearisation of  at these two vacua reveals that one of them is a source while the other is a sink. The differential equations  is a Hamiltonian flow for the 