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  An algebraic scheme associated with the noncommutative KP hierarchy and some of its extensions

Dimakis, A., & Müller-Hoissen, F. (2005). An algebraic scheme associated with the noncommutative KP hierarchy and some of its extensions. Journal of Physics A: Mathematical and General, 38, 5453-5505. doi:10.1088/0305-4470/38/24/005.

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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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Free keywords: KP hierarchy; trace method; shuffle; Rota-Baxter; deformation
 Abstract: A well-known ansatz (`trace method') for soliton solutions turns the equations of the (noncommutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. We develop an algebraic formalism, in particular involving a (mixable) shuffle product, to explore their structure. More precisely, we show that the equations of the noncommutative KP hierarchy and its extension (xncKP) in the case of a Moyal-deformed product, as derived in previous work, correspond to identities in this algebra. Furthermore, the Moyal product is replaced by a more general associative product. This leads to a new even more general extension of the noncommutative KP hierarchy. Relations with Rota-Baxter algebras are established.

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Language(s): eng - English
 Dates: 2005-06-01
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: eDoc: 241892
DOI: 10.1088/0305-4470/38/24/005
 Degree: -

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Title: Journal of Physics A: Mathematical and General
  Alternative Title : J. Phys. A: Math. Gen.
Source Genre: Journal
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Publ. Info: -
Pages: - Volume / Issue: 38 Sequence Number: - Start / End Page: 5453 - 5505 Identifier: -