Functional representations of integrable hierarchies

Abstract

We consider a general framework for integrable hierarchies in Lax form and derive certain universal equations from which `functional representations' of particular hierarchies (like 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' analogs of `Fay identities' for the KP hierarchy.

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

References in corpus (1)

• Spitzer's Identity and the Algebraic Birkhoff Decomposition in pQFT

Cited by in corpus (4)

• With a Cole-Hopf transformation to solutions of the noncommutative KP hierarchy in terms of Wronski matrices
• Burgers and KP hierarchies: A functional representation approach
• 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