1996/04/23 by Ian A. B. Strachan, I. A. B. Strachan · 66 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Associative property #Differential calculus #Differential form #Differential geometry #Differential operator #Hamiltonian (control theory) #Hamiltonian system #Hierarchy #Homotopy and Cohomology in Algebraic Topology #Integrable system #Limit (mathematics) #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Star product #Vector calculus #hep-th #nlin.SI #solv-int
paper · pdf · doi:10.1016/s0393-0440(96)00019-8
published in Journal of Geometry and Physics 21(3), 255-278 (Elsevier BV) · LaTeX, 29 pages. To be published in J.Geom.Phys
arxiv created 1996/04/23 · openalex publication_date 1997/02/01 · arxiv updated 2020/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one obtains a geometric description of the operators. A dual theory is also possible, based on a deformation of differential forms. This calculus is applied to a number of multidimensional integrable systems, such as the KP hierarchy, thus obtaining a geometrical description of these systems. The limit in which the deformation disappears corresponds to taking the dispersionless limit in these hierarchies.