$n$ anti-solitons, interpolating between all neighbouring pairs of vacua as in the previous two cases.

For $SO(2)$ models, the charge $Q$  is equal to the topological charge $Q_T$ . The value of $Q$ for the solitons is $$Q=\mp {4\over n} \bigg[\sqrt{1-\kappa^2}+\kappa\, {\rm arc}
\sin(\kappa)+\xi\, {\kappa\over2}\pi\bigg]
\ ,
\eqn\sevenc$$ where $\xi$ is either minus or plus, ($\xi=\mp$); $Q$ for $\xi=-$ is the charge of  solutions and $Q$ for $\xi=+$ is the charge of  solutions. From this, it is straightforward to compute the mass of the solitons to find $$E={2 m\over n}\bigg[\sqrt{1-\kappa^2}+\kappa\, {\rm
arc}\sin(\kappa)+\xi\, {\kappa\over2}\pi\bigg]\ .
\eqn\eightc$$ The $SO(2)$ solitons  and  have one moduli parameter $x_0$. Using , the metric on the moduli space is $$ds^2={ m\over n}\bigg[\sqrt{1-\kappa^2}+\kappa\, {\rm arc}
\sin(\kappa)+\xi\, {\kappa\over2}\pi\bigg]
dx_0^2={E\over 2} dx_0^2\ .
\eqn\ninec$$ The charge, the mass and the moduli metric of the solitons   are derived by setting $\kappa=0$ in the above corresponding expressions.

Finally, the charge, the mass and the moduli metric of the solutions   of models with $\kappa=1$ are $$Q=\mp {4\over n} \pi\ ,
\eqn\tenc$$ $$E={2 m\over n} \pi\ ,
\eqn\tencc$$ and $$ds^2={m\over n} \pi dx_0^2={E\over2} dx_0^2\ ,
\eqn\tenccc$$ respectively.

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

A parameterisation of $SU(2)$ in terms of $2\times2$ matrices is $$k=\pmatrix{M+iN &\quad 