Topological Field Theory approach to the Generalized Benney Hierarchy
Jen-Hsu Chang, Ming-Hsien Tu

TL;DR
This paper explores the integrability of the generalized Benney hierarchy using topological field theory methods, deriving free energy, correlation functions, and genus-one corrections to its Poisson brackets.
Contribution
It introduces a novel approach linking topological field theories with the generalized Benney hierarchy, including genus-one corrections and explicit formulations.
Findings
Primary free energy and correlation functions at genus zero are obtained.
Genus-one corrections to the Poisson brackets are explicitly derived.
The approach connects Landau-Ginzburg formulation with integrable hierarchy analysis.
Abstract
The integrability of the generalized Benney hierarchy with three primary fields is investigated from the point of view of two-dimensional topological field theories coupled to gravity. The associated primary free energy and correlation functions at genus zero are obtained via Landau-Ginzburg formulation and the string equation is derived using the twistor construction for the Orlov operators. By adopting the approach of Dubrovin and Zhang we obtain the genus-one corrections of the Poisson brackets of the generalized Benney hierarchy.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory
