The extended D-Toda hierarchy
Jipeng Cheng, Todor Milanov
TL;DR
This paper introduces the extended D-Toda hierarchy, a new integrable system of Lax equations linked to the Gromov--Witten theory of Fano orbifold lines of type D, expanding the understanding of integrable hierarchies in algebraic geometry.
Contribution
It establishes the extended D-Toda hierarchy as the Lax equation system corresponding to solutions of Hirota Bilinear Equations for Fano orbifold lines of type D.
Findings
Every solution to Hirota Bilinear Equations yields a solution to the extended D-Toda hierarchy.
The extended D-Toda hierarchy generalizes Carlet's extended bi-graded Toda hierarchy.
The hierarchy is connected to Gromov--Witten theory of Fano orbifold lines of type D.
Abstract
In a companion paper to this one, we proved that the Gromov--Witten theory of a Fano orbifold line of type is governed by a system of Hirota Bilinear Equations. The goal of this paper is to prove that every solution to the Hirota Bilinear Equations determines a solution to a new integrable hierarchy of Lax equations. We suggest the name extended D-Toda hierarchy for this new system of Lax equations, because it should be viewed as the analogue of Carlet's extended bi-graded Toda hierarchy, which is known to govern the Gromov--Witten theory of Fano orbifold lines of type
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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models