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arXiv · 1511.05245

Integrability of the Frobenius algebra-valued KP hierarchy

Ian A. B. Strachan·Dafeng Zuo
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Abstract

We introduce a Frobenius algebra-valued KP hierarchy and show the existence of Frobenius algebra-valued $τ$-function for this hierarchy. In addition we construct its Hamiltonian structures by using the Adler-Dickey-Gelfand method. As a byproduct of these constructions, we show that the coupled KP hierarchy defined by P.Casati and G.Ortenzi in \cite{CO2006} has at least $n$-``basic" different local bi-Hamiltonian structures. Finally, via the construction of the second Hamiltonian structures, we obtain some local matrix, or Frobenius algebra-valued, generalizations of classical $W$-algebras.

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Ian A. B. Strachan, Dafeng Zuo. 2015-11-17. Integrability of the Frobenius algebra-valued KP hierarchy. https://doi.org/10.1063/1.4935936

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