A notion of complete integrability in noncommutative geometry and the Korteweg-de-Vries equation
نویسنده
چکیده
We introduce a new concept of complete integrability in the framework of noncommutative geometry. It involves a gauged bi-differential calculus over an associative (and not necessarily commutative) algebra A. Basically, this is an N0-graded left A-module with two covariant exterior derivatives acting on it which, as a consequence of certain (e.g., nonlinear differential) equations, are flat and anticommute. As an example, we associate a gauged bi-differential calculus with the KdV equation and compute its conserved densities.
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تاریخ انتشار 1999