A note on the extended dToda hierarchy
Niann-Chern Lee, Ming-Hsien Tu

TL;DR
This paper derives dispersionless Hirota equations for the extended dispersionless Toda hierarchy, linking them to topological recursion in the $CP^1$ model, and computes two-point functions involving Catalan numbers.
Contribution
It provides a novel derivation of dispersionless Hirota equations from topological recursion relations for the extended Toda hierarchy.
Findings
Dispersionless Hirota equations are derived from topological recursion.
Two-point functions are computed and expressed via Catalan numbers.
The work connects integrable hierarchies with topological field theory.
Abstract
We give a derivation of dispersionless Hirota equations for the extended dispersionless Toda hierarchy. We show that the dispersionless Hirota equations are nothing but a direct consequence of the genus-zero topological recursion relation for the topological model. Using the dispersionless Hirota equations we compute the two point functions and express the result in terms of Catalan number.
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Taxonomy
TopicsElectoral Systems and Political Participation · Algorithms and Data Compression
