2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/50824The 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.26 pages, RevtexHigh Energy Physics - Theorytext