Integrable models as constrained topological gauge theory

Integrable models in 1+1 dimensions are related to the hierarchy of gauge fixing constraints for BF topological gauge theory. The gauge equivalent systems for Zweibein fields are described by a pair of time reserved nonlinear equations as in termo-field theory. For the related Lax pair the spectral parameter must appear as a constant valued spin connection associated with Abelian gauge symmetry. Dissipative structures with integrable dynamics in the gauge theory of gravity are discussed as well as the 2+1 dimensional extension to the Chern-Simons theory.