Integrability of the Frobenius algebra-valued Kadomtsev-Petviashvili hierarchy
Integrability of the Frobenius algebra-valued Kadomtsev-Petviashvili hierarchy
We introduce a Frobenius algebra-valued Kadomtsev-Petviashvili (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 Casati and Ortenzi [J. …