Field theories with an infinite number of conservation laws and Bäcklund transformations in two dimensions

Field theories in two dimensions are generated from the integrability condition of a linear system which possesses Poincaré and internal symmetries. From matrix solutions of this system we get (i) an infinite set of non-local conserved currents and (ii) a family of one-parameter Bäcklund transformations. A large class of models is covered here, as the non-linear sigma, the SU(n) ? SU(n) and the non-abelian gauge invariant projector models.