1999/08/31 by Aristophanes Dimakis, Folkert Muller-Hoissen, Folkert Müller-Hoissen
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic differential equation #Algebraic structures and combinatorial models #Associative property #Black Holes and Theoretical Physics #Commutative property #Covariant transformation #Differential (mechanical device) #Differential algebraic equation #Differential calculus #Differential equation #Korteweg–de Vries equation #Mathematical analysis #Mathematical physics #Mathematics #Multivariable calculus #Nonlinear Waves and Solitons #Nonlinear system #Ordinary differential equation #Physics #Pure mathematics #Time-scale calculus #math-ph #math.DG #math.MP
paper · pdf · doi:10.1016/s0034-4877(01)80024-0
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"
arxiv created 1999/09/19 · openalex publication_date 2000/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.