Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hirota Quadratic Equations for the Extended Toda Hierarchy   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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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph