  We use the methods of group theory to reduce the equations of motion of the
$CP^{1}$ model in (2+1) dimensions to sets of two coupled ordinary differential
equations. We decouple and solve many of these equations in terms of elementary
functions, elliptic functions and Painlev{\'e} transcendents. Some of the
reduced equations do not have the Painlev{\'e} property thus indicating that
the model is not integrable, while it still posesses many properties of
integrable systems (such as stable ``numerical'' solitons).
