Bi-differential calculi and integrable models

Details Bi-differential calculi and integrable models Bi-differential calculi and integrable models

1999-08-11

arxiv.org/abs/math-ph/9908015v2

Physics

Mathematical Physics

24 pages, 2 figures, uses amssymb.sty and diagrams.sty, substantial extensions of examples (relative to first version)

Scientific paper

10.1088/0305-4470/33/5/311

The existence of an infinite set of conserved currents in completely integrable classical models, including chiral and Toda models as well as the KP and self-dual Yang-Mills equations, is traced back to a simple construction of an infinite chain of closed (respectively, covariantly constant) 1-forms in a (gauged) bi-differential calculus. The latter consists of a differential algebra on which two differential maps act. In a gauged bi-differential calculus these maps are extended to flat covariant derivatives.

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