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  Weakly nonassociative algebras, Riccati and KP hierarchies

Dimakis, A., & Müller-Hoissen, F. (2009). Weakly nonassociative algebras, Riccati and KP hierarchies. In S. Silvestrov, E. Paal, V. Abramov, & A. Stolin (Eds.), Generalized Lie Theory in Mathematics, Physics and Beyond (pp. 9-27). Berlin Heidelberg: Springer-Verlag.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-1335-C Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-1336-A
Genre: Book Chapter

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 Creators:
Dimakis, Aristophanes, Author
Müller-Hoissen, Folkert1, Author              
Affiliations:
1Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063285              

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 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 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.

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Language(s): eng - English
 Dates: 2009
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: eDoc: 403450
 Degree: -

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Title: Generalized Lie Theory in Mathematics, Physics and Beyond
Source Genre: Book
 Creator(s):
Silvestrov, S., Editor
Paal, E., Editor
Abramov, V., Editor
Stolin, A., Editor
Affiliations:
-
Publ. Info: Berlin Heidelberg : Springer-Verlag
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 9 - 27 Identifier: -