BI-DIFFERENTIAL CALCULUS AND THE KDV EQUATION

A gauged bi-differential calculus over an associative (and not Anecessarily commutative) algebra A is an No-graded left A-module with Atwo covariant derivatives acting on it which, as a consequence of Acertain (e.g. nonlinear differential) equations, are flat and anticommute. As a consequence, there is an iterative Aconstruction of generalized conserved currents. We associate a gauged Abi-differeritial calculus with the Korteweg-de Vries equation and use Ait to compute conserved densities of this equation.