into the second equation of \oneb, it reduces to 
$$
{d \over dx}k(x)=\mp {m\over2} \big(\kappa k(x)+k(x) \kappa +k(x)
\sum_A t_A {\rm tr}(t_A
k^n(x))\big)\ .
\eqn\threeb 
$$
This is a non-linear but ordinary differential equation and the 
investigation of its solutions for various
choices of $G$ and $n$ will be our task in the rest of the paper. 

It is sufficient to investigate \threeb\ for
$n&gt;0$ because the transformation
$$
k\rightarrow k^{-1}, \qquad x\rightarrow -x 
\eqn\fiveba
$$
acting on a model with coupling constants $g, b,, m$  and
$a=[1n]{}[tr]{} k\^n$ transforms it to a
model with coupling constants $g, b,, m$ and
$a=-[1n]{}[tr]{} k\^[-n]{}$.  Therefore the solitons of models 
with $n&lt;0$  can be obtained from
the solitons of models with $n&gt;0$ by acting on the latter with \fiveba.  
In addition, the Lagrangian \onebb, the field equations and the
Bogomol'nyi equations of the
(1,1)-supersymmetric sigma model are invariant under the sigma model symmetry
$$
k(x,t)\rightarrow h k(x,t) h^{-1} \qquad \kappa\rightarrow h \kappa h^{-1}\ ,
\eqn\fiveb
$$
 where $hG$.  Although sigma
model symmetries are not associated with conserved charges, we can use
\fiveb\ to choose, without loss of
generality, the coupling constant $$ in the Cartan subalgebra of
$[L]{} (G)$. This choice
of 