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

Dimakis, Aristophanes; Müller-Hoissen, Folkert

doi:10.1088/0305-4470/38/24/005

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

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

MPS-Authors

/persons/resource/persons173596

Müller-Hoissen, Folkert
Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

External Resource

No external resources are shared

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

There are no public fulltexts stored in PuRe

Supplementary Material (public)

There is no public supplementary material available

Citation

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.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-1587-A

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.