Bi-differential calculus and the KdV equation

Details Bi-differential calculus and the KdV equation Bi-differential calculus and the KdV equation

1999-08-17

arxiv.org/abs/math-ph/9908016v2

Physics

Mathematical Physics

9 pages, LaTeX, uses amssymb.sty, XXXI Symposium on Mathematical Physics, Torun, May 1999, replaces "A notion of complete inte

Scientific paper

10.1016/S0034-4877(01)80024-0

A gauged bi-differential calculus over an associative (and not necessarily commutative) algebra A is an N-graded left A-module with two covariant derivatives acting on it which, as a consequence of certain (e.g., nonlinear differential) equations, are flat and anticommute. As a consequence, there is an iterative construction of generalized conserved currents. We associate a gauged bi-differential calculus with the Korteweg-de-Vries equation and use it to compute conserved densities of this equation.

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