Abstract
The extended Toda hierarchy (ETH) was introduced by E. Getzler [Ge] and independently by Y. Zhang [Z] in order to describe an integrable hierarchy that governs the Gromov-Witten invariants of . The Lax-type presentation of the ETH was given in [CDZ]. In this article, we give a description of the ETH in terms of tau functions and Hirota quadratic equations (HQEs), also known as Hirota bilinear equations (HBEs). 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
Citation
Todor E. Milanov. "Hirota quadratic equations for the extended Toda hierarchy." Duke Math. J. 138 (1) 161 - 178, 15 May 2007. https://doi.org/10.1215/S0012-7094-07-13815-8
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