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  Algebraic identities associated with KP and AKNS hierarchies

Dimakis, A., & Müller-Hoissen, F. (2005). Algebraic identities associated with KP and AKNS hierarchies. Czechoslovak Journal of Physics, 55(11), 1385-1390.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-1545-B Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-1546-9
Genre: Journal Article

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

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 Abstract: We present an overview of recent results (nlin.SI/0501003, J.Phys.A: Math.Gen. 38 (2005) 5453). An old (``trace") method of Okhuma and Wadati to generate soliton solutions of the KP equation via a formal power series ansatz leads to a correspondence between algebraic partial sum identities and the equations of the classical KP hierarchy (where the fields are allowed to have values in an arbitrary associative algebra). Moreover, such a correspondence can be achieved by abstracting from the partial sum calculus to an algebraic scheme, which in particular involves a (mixable) shuffle product and makes contact with Rota-Baxter algebras. Furthermore, larger sets of identities in this algebra correspond to extensions of the KP hierarchy in the case where the associative product is a Moyal-product or a certain generalization of it.

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Language(s): eng - English
 Dates: 2005-11
 Publication Status: Published in print
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 Identifiers: eDoc: 250129
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Title: Czechoslovak Journal of Physics
  Alternative Title : Czech. J. Phys.
Source Genre: Journal
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Pages: - Volume / Issue: 55 (11) Sequence Number: - Start / End Page: 1385 - 1390 Identifier: -