Hirota quadratic equations for the extended Toda hierarchy
By T. Milanov. 2005
55 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Spectroscopy, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b78cac8c9fcb6a5f1e789cd893d3361b32b2e45a
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In Geometry and Topology
In Spectroscopy
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Citations in the corpus
- The spaces of Laurent polynomials, Gromov-Witten theory of ℙ1-orbifolds and integrable hierarchies (2008, background): “The results of this paper suggest that we can add one more pair to the above list: — Orbifold quantum cohomology of Ck;m and the extended bi-graded Toda hierarchy.”