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

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Cited by in corpus (12)

• Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions
• Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation
• Self-Consistent Sources for Integrable Equations via Deformations of Binary Darboux Transformations
• 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
• Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation
• Functional representation of the negative AKNS hierarchy
• Integrable discrete systems on R and related dispersionless systems
• Dispersionless limit of the noncommutative potential KP hierarchy and solutions of the pseudodual chiral model in 2+1 dimensions
• Bi-Hamiltonian structures for integrable systems on regular time scales
• Bäcklund transformations between the AKNS and DNLS hierarchies