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Hirota Quadratic Equations for the Extended Toda Hierarchy

Todor E. Milanov
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Abstract

The Extended Toda Hierarchy (shortly ETH) was introduce by E. Getzler \cite{Ge} and independently by Y. Zhang \cite{Z} in order to describe an integrable hierarchy which governs the Gromov--Witten invariants of $\C P^1$. The {\em Lax type} presentation of the ETH was given in \cite{CDZ}. In this paper we give a description of the ETH in terms of {\em tau-functions} and Hirota Quadratic Equations (known also as Hirota Bilinear Equations). A new feature here is that the Hirota equations are given in terms of vertex operators taking values in the algebra of differential operators on the affine line.

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Todor E. Milanov. 2006-04-29. Hirota Quadratic Equations for the Extended Toda Hierarchy. https://arxiv.org/abs/math/0501336

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