1999/08/31 by Aristophanes Dimakis, Folkert Muller-Hoissen, Folkert Müller-Hoissen · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic differential equation #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Computer science #Constant (computer programming) #Covariant transformation #Differential (mechanical device) #Differential algebra #Differential algebraic equation #Differential calculus #Differential equation #Differential form #Dual (grammatical number) #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Ordinary differential equation #Physics #Pure mathematics #Simple (philosophy) #gr-qc #hep-th #math-ph #math.MP #nlin.SI #solv-int
paper · pdf · doi:10.1088/0305-4470/33/5/311
24 pages, 2 figures, uses amssymb.sty and diagrams.sty, substantial extensions of examples (relative to first version)
arxiv created 1999/11/10 · openalex publication_date 2000/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.