Bihamiltonian structure of the $(n,1)$-type rational reductions of the 2D-Toda hierarchy

Abstract

We derive a local bihamiltonian structure for the rational reduction of the 2D-Toda hierarchy (RR2T) of $(n,1)$-type by direct computations, and construct an $(n+1)$-dimensional semisimple generalized Frobenius manifold with non-flat unity whose Principal Hierarchy contains its dispersionless flows.

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