Weakly Nonassociative Algebras, Riccati and KP Hierarchies

Aristophanes Dimakis () and Folkert Müller-Hoissen ()
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Aristophanes Dimakis: University of the Aegean, Department of Financial and Management Engineering
Folkert Müller-Hoissen: Max-Planck-Institute for Dynamics and Self-Organization, Bunsenstrasse 10

Chapter 2 in Generalized Lie Theory in Mathematics, Physics and Beyond, 2009, pp 9-27 from Springer

Abstract: It has recently been observed that certain nonassociative algebras (called ‘weakly nonassociative‐, WNA) determine, via a universal hierarchy of ordinary differential equations, solutions of the KP hierarchy with dependent variable in an associative subalgebra (the middle nucleus). We recall central results and consider a class of WNA algebras for which the hierarchy of ODEs reduces to a matrix Ric-cati hierarchy, which can be easily solved. The resulting solutions of a matrix KP hierarchy determine, under a ‘rank one condition’, solutions of the scalar KP hierarchy. We extend these results to the discrete KP hierarchy. Moreover, we build a bridge from the WNA framework to the Gelfand—Dickey—Sato formulation of the KP hierarchy.

Keywords: Integrable Hierarchy; Riccati Differential Equation; Nonassociative Algebra; Matrix Riccati Equation; Lump Solution (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-85332-9_2

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DOI: 10.1007/978-3-540-85332-9_2

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