Bi-differential calculus and the KdV equation (Q5942385)

The existence of a gauged bi-differential calculus as a (nontrivial) consequence of certain equations may turn out to be a common feature of completely integrable systems. The authors consider the notion of a (gauged) bi-differential calculus and its generalization and applies it to a large variety of structures (based on noncommutative algebras) most of which are far away from classical completely integrable models. Moreover they associate a gauged bi-differential calculus wit KdV equation and use it to compute conserved densities of this equation.