2007/03/21 by Aristophanes Dimakis, Folkert Muller-Hoissen, Folkert Müller-Hoissen
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math-ph #math.MP #msc:17D99 #msc:35Q53 #msc:35Q58 #nlin.SI
paper · pdf · doi:10.1088/1751-8113/40/27/010
25 pages
arxiv created 2007/03/21 · openalex publication_date 2007/06/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Partly inspired by Sato's theory of the Kadomtsev–Petviashvili (KP) hierarchy, we start with a quite general hierarchy of linear ordinary differential equations in a space of matrices and derive from it a matrix Riccati hierarchy. The latter is then shown to exhibit an underlying 'weakly nonassociative' (WNA) algebra structure, from which we can conclude, referring to previous work, that any solution of the Riccati system also solves the potential KP hierarchy (in the corresponding matrix algebra). We then turn to the case where the components of the matrices are multiplied using a (generalized) star product. Associated with the deformation parameters, there are additional symmetries (flow equations) which enlarge the respective KP hierarchy. They have a compact formulation in terms of the WNA structure. We also present a formulation of the KP hierarchy equations themselves as deformation flow equations.