of the solutions  is again a cylinder with co-ordinates $(x_0, \psi)$ and with metric $$ds^2=e^\sigma {\sqrt{1-\kappa^2}\over m
(1+\alpha^2 \kappa^2)}\bigg[m^2 
(1-\kappa^2+\alpha^2\kappa^2)  dx_0^2+ d\psi^2\bigg]\ .
\eqn\mfived$$ We remark that there is a transformation of the moduli co-ordinates $(x_0, \psi)\rightarrow (y, \chi)$ such that the moduli space metric above can be written in the form $ds^2={E\over2}(dy^2+d\chi^2)$.

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

To show that all solitons of the $SU(2)$ $n=2$ model lie on the maximal torus of $SU(2)$, we begin from the equations  for $M,N$ with $n=2$ $$\eqalign{
{d\over dx}M\pm m [-\kappa N+2(1-M^2)M]&=0
\cr
{d\over dx}N\pm m[\kappa M-2NM^2]&=0 \ .}
\eqn\fived$$ We then use the field redefinitions $$X={N\over M}, \qquad Y={N\over \sqrt {1-M^2}}
\eqn\tend$$ to simplify  to $$\eqalign{
{d\over dx}X\pm  m\big[ \kappa (1+X^2)-2X\big]&=0
\cr
{d\over dx}Y\pm  m \kappa X^{-1} Y [1-Y^2]&=0\ .}
\eqn\elevend$$ The solutions in terms of $X,Y$ for $0<\kappa<1$ are $$\eqalign{
X&={1\over \kappa}\bigg(1+\sqrt{1-\kappa^2} \tanh\big(\pm m 
\sqrt{1-\kappa^2}(x-x_0)\big) \bigg)
\cr
{Y^2\over 1-Y^2}&={\rho}^{-1} X^2 \exp\big(\mp 2m (x-x_0)\big)\cosh^2\big(
m\sqrt{1-\kappa^2} (x-x_0)\big)\ ,}
\eqn\twelved$$ and $$\eqalign{
X&={1\over \kappa}\bigg(1+\sqrt{1-\kappa^2} \coth \big(\pm m 
\sqrt{1-\kappa^2} (x-x_0)\big) \bigg)
\cr
{Y^2\over 1-Y^2}&={\rho}^{-1} X^2 \exp\big(\mp 2m (x-x_0)\big) \sinh^2\big(
m\sqrt{1-\kappa^2} (x-x_0)\big)\ ,}
\eqn\twelved$$ where $\rho, x_0$ are real constants ($\rho\geq 0$). It remains to examine whether or not these solutions interpolate between the different 