Principal hierarchies of infinite-dimensional Frobenius manifolds: the extended 2D Toda lattice

Details Principal hierarchies of infinite-dimensional Frobenius manifolds: the extended 2D Toda lattice Principal hierarchies of infinite-dimensional Frobenius manifolds: the extended 2D Toda lattice

2011-09-25

arxiv.org/abs/1109.5343v2

Physics

Mathematical Physics

47 pages

Scientific paper

We define a dispersionless tau-symmetric bihamiltonian integrable hierarchy on the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/$\infty$ respectively, which extends the dispersionless 2D Toda hierarchy of Takasaki and Takebe. Then we construct the deformed flat connection of the infinite-dimensional Frobenius manifold $M_0$ introduced in [4] and, by explicitly solving the deformed flatness equations, we prove that the extended 2D Toda hierarchy coincides with principal hierarchy of $M_0$.

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