  We analyze the symplectic structure on the dressing group in the \shG\, model
by calculating explicitly the Poisson bracket $\{g\x g\}$ where $g$ is the
\dg\, element which creates a generic one soliton solution from the vacuum. Our
result is that this bracket does not coincide with the Semenov--Tian--Shansky
one. The last induces a Lie--Poisson structure on the \dg . To get the bracket
obtained by us from the Semenov--Tian--Shansky bracket we apply the formalism
of the constrained Hamiltonian systems. The constraints on the \dg\, appear
since the element which generates one solitons from the vacuum has a specific
form.

High Energy Physics - Theory