English

Bi-differential calculus and the KdV equation

Mathematical Physics 2009-10-31 v2 Differential Geometry math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.math-ph/9908016,
  title  = {Bi-differential calculus and the KdV equation},
  author = {Aristophanes Dimakis and Folkert Muller-Hoissen},
  journal= {arXiv preprint arXiv:math-ph/9908016},
  year   = {2009}
}

Comments

9 pages, LaTeX, uses amssymb.sty, XXXI Symposium on Mathematical Physics, Torun, May 1999, replaces "A notion of complete integrability in noncommutative geometry and the Korteweg-de-Vries equation"