  As a prototype of powerful non-abelian symmetry in an Integrable System, I
will show the appearance of a Witt algebra of vector fields in the SG theory.
This symmetry does not share anything with the well-known Virasoro algebra of
the conformal $c=1$ unperturbed limit. Although it is quasi-local in the SG
field theory, nevertheless it gives rise to a local action on $N$-soliton
solution variables. I will explicitly write the action on special variables,
which possess a beautiful geometrical meaning and enter the Form Factor
expressions of quantum theory. At the end, I will also give some preliminary
hints about the quantisation.
