Abstract
The existence of an infinite set of conserved currents in completely integrable classical models, including chiral and Toda models as well as the KP and self-dual Yang-Mills equations, is traced back to a simple construction of an infinite chain of closed (respectively, covariantly constant) 1-forms in a (gauged) bi-differential calculus. The latter consists of a differential algebra on which two differential maps act. In a gauged bi-differential calculus these maps are extended to flat covariant derivatives.
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