Functional representations of integrable hierarchies

2006/03/11 by Aristophanes Dimakis, Folkert Muller-Hoissen, Folkert Müller-Hoissen · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1088/0305-4470/39/29/012

21 pages, version 2: equations (3.28) and (4.11) added

arxiv created 2006/03/11 · openalex publication_date 2006/07/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We consider a general framework for integrable hierarchies in Lax form and derive certain universal equations from which 'functional representations' of particular hierarchies (such as KP, discrete KP, mKP, AKNS), i.e. formulations in terms of functional equations, are systematically and quite easily obtained. The formalism genuinely applies to hierarchies where the dependent variables live in a noncommutative (typically matrix) algebra. The obtained functional representations can be understood as 'noncommutative' analogues of 'Fay identities' for the KP hierarchy.

Citations

• Integrable Hierarchies and Dispersionless Limit
• Spitzer's identity and the algebraic Birkhoff decomposition in pQFT

Cited by

• From AKNS to derivative NLS hierarchies via deformations of associative products
• Dispersionless limit of the noncommutative potential KP hierarchy and solutions of the pseudodual chiral model in 2 + 1 dimensions
• Burgers and Kadomtsev-Petviashvili hierarchies: A functional representation approach