2005/01/31 by Aristophanes Dimakis, Folkert Muller-Hoissen, Folkert Müller-Hoissen · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebra representation #Algebraic number #Algebraic structures and combinatorial models #Ansatz #Associative algebra #Commutative property #Computer science #Division algebra #Extension (predicate logic) #Formalism (music) #Hierarchy #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative algebraic geometry #Noncommutative geometry #Noncommutative quantum field theory #Nonlinear Waves and Solitons #Pure mathematics #TRACE (psycholinguistics) #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1088/0305-4470/38/24/005
published as J.Phys. A38 (2005) 5453-5506 · 59 pages, relative to the second version a few minor corrections, but quite a lot of amendments, to appear in J. Phys. A
arxiv created 2005/05/09 · openalex publication_date 2005/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A well-known ansatz ('trace method') for soliton solutions turns the equations of the (non-commutative) 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 non-commutative 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 non-commutative KP hierarchy. Relations with Rota–Baxter algebras are established.