On the Benney Hierarchy: free energy, string equation and quantization

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dc.creatorChang, Jen-Hsu
dc.creatorTu, Ming-Hsien
dc.date2000-09-13
dc.date.accessioned2026-07-07T10:54:21Z
dc.date.available2026-07-07T10:54:21Z
dc.descriptionThe bi-Hamiltonian structure of the Benney hierarchy is revisited. We show that the compatibility condition of the Poisson brackets provides the genus zero free energy of a topological field theory coupled to 2d gravity. We calculate the correlation functions via the Landau-Ginzburg formulation and derive the string equation based on the twistor construction. Moreover, by using the approach of Dubrovin and Zhang, we compute the genus one correction of the Poisson brackets and compare them with the Oevel-Strampp's brackets of the Kaup-Broer hierarchy.
dc.description28 pages, RevTex
dc.identifierhttps://arxiv.org/abs/nlin/0009026
dc.identifierhttp://arxiv.org/abs/nlin/0009026
dc.identifierJ.Phys.A34:251-272,2001
dc.identifierdoi:10.1088/0305-4470/34/2/304
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185776
dc.subjectExactly Solvable and Integrable Systems
dc.titleOn the Benney Hierarchy: free energy, string equation and quantization
dc.typetext

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