include the solution
given in [\gptb]. In the
$n=2$ case, we shall show that all solitons which lie on the maximal  
torus are obtained from embedding
of $SO(2)$ solitons into the $SU(2)$ model. 
In addition, we shall examine the qualitative properties of the Bogomol'nyi
equations for $SU(2)$  $n&gt;2$ models and support our conclusions with a
numerical calculation for the $n=3, 4, 5$ cases (Fig [1,2,3]).
Finally, we shall show that the $G$-model for
$G$ any semisimple Lie group has static and time-dependent solutions.
The former lie on the maximal torus
of $G$ while the latter lie on the complement of the maximal torus.
Some of the $G$-model solitons 
are obtained from embedding $SO(2)$ and $SU(2)$ solitons.

The organisation of the paper is as follows:  In section two, we shall
introduce the Bogomol'nyi equations of
$G$-models and discuss their general properties. In section
three,  we shall solve the Bogomol'nyi equations for $G=SO(2)$ and
compute the charge, mass and moduli space
metric of the solitons. In section four, we shall examine the general
properties of the $SU(2)$ model
and give all static solitons that lie on the maximal torus of $SU(2)$.
In section five, we shall investigate
the time-dependent solitons  of the
