  The classical spin model in planar condensed media is represented as the U(1)
Chern-Simons gauge field theory. When the vorticity of the continuous flow of
the media coincides with the statistical magnetic field, which is necessary for
the model's integrability, the theory admits zero curvature connection. This
allows me to formulate the model in terms of gauge - invariant fields whose
evolution is described by the Davey-Stewartson (DS) equations. The Self-dual
Chern-Simons solitons described by the Liouville equation are subjected to
corresponding integrable dynamics. As a by-product the 2+1-dimensional
zero-curvature representation for the DS equation is obtained as well as the
new reduction conditions related to the DS-I case. Some possible applications
for the statistical transmutation in the anyon superfluid and TQFT are briefly
discussed.
