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

2000/09/13 by Jen-Hsu Chang, Ming-Hsien Tu · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #nlin.SI

paper · pdf · doi:10.1088/0305-4470/34/2/304

published as J.Phys.A34:251-272,2001 · 28 pages, RevTex

arxiv created 2000/09/13 · openalex publication_date 2001/01/03 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

The 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 two-dimensional 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 brackets of the Kaup-Broer hierarchy.

Citations

• INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• Dispersionful analogues of Benney's equations and N -wave systems
• Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II

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