Weakly nonassociative algebras, Riccati and KP hierarchies

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dc.creatorDimakis, Aristophanes
dc.creatorMuller-Hoissen, Folkert
dc.date2007-01-04
dc.date2008-01-16
dc.date.accessioned2026-07-07T08:54:41Z
dc.date.available2026-07-07T08:54:41Z
dc.descriptionIt 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 Riccati hierarchy, which can be easily solved. The resulting solutions of a matrix KP hierarchy then determine (under a rank 1 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 formulation of the KP hierarchy.
dc.description16 pages, second version: LaTeX problem with L's in section 5 resolved, third version: example 2 in section 3 added, some minor corrections, forth version: a few small changes and corrections. Proceedings of the workshop Algebra, Geometry, and Mathematical Physics, Lund, October, 2006
dc.identifierhttps://arxiv.org/abs/nlin/0701010
dc.identifierhttp://arxiv.org/abs/nlin/0701010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146026
dc.subjectExactly Solvable and Integrable Systems
dc.subjectMathematical Physics
dc.titleWeakly nonassociative algebras, Riccati and KP hierarchies
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