On the Benney Hierarchy: free energy, string equation and quantization
Exactly Solvable and Integrable Systems
2008-11-26 v1
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 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.
Cite
@article{arxiv.nlin/0009026,
title = {On the Benney Hierarchy: free energy, string equation and quantization},
author = {Jen-Hsu Chang and Ming-Hsien Tu},
journal= {arXiv preprint arXiv:nlin/0009026},
year = {2008}
}
Comments
28 pages, RevTex