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Journal Article

Functional representations of integrable hierarchies


Müller-Hoissen,  Folkert
Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Dimakis, A., & Müller-Hoissen, F. (2006). Functional representations of integrable hierarchies. Journal of Physics A: Mathematical and General, 39, 9169-9186.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-14CB-9
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.