On the Hamiltonian Representation of the Associativity Equations
We demonstrate that for an arbitrary number n of primary fields the equations of the associativity can be rewritten in the form of (n — 2) pairwise commuting systems of hydrodynamic type, which appear to be nondiagonalizable but integrable. We propose a natural Hamiltonian representation of the systems under study in the cases n = 3 and n = 4.
KeywordsHamiltonian System Poisson Bracket Spectral Problem Hamiltonian Structure Hydrodynamic Type
Unable to display preview. Download preview PDF.
- Dubrovin, B., Geometry of 2D topological field theories, preprint SISSA- 89/94/FM, SISSA, Trieste (1994).Google Scholar
- Mokhov, O.I., Differential equations of associativity in 2D topological field theories and geometry of nondiagonalizable systems of hydrodynamic type, In: Abstracts of Internat. Conference on Integrable Systems “Nonlinearity and Integrability: from Mathematics to Physics”, February 21-24, 1995, Montpellier, France (1995).Google Scholar
- Mokhov, O.I., Symplectic and Poisson geometry on loop spaces of manifolds and nonlinear equations, AMS Translations, series 2 Vol. 170 Topics in topology and mathematical physics, S.P. Novikov, ed., (1995); hep-th/9503076.Google Scholar
- Tsarev, S.P., Geometry of Hamiltonian systems of hydrodynamic type, The generalized hodograph method, Izvestiya Akad. Nauk SSSR, Ser. mat. 54 (5) (1990), 1048 - 1068.Google Scholar
- Dijkgraaf, R., Verlinde, H., and Verlinde, E., Topological string in gravity, Nucl. Physics B 352 (1991), 59-86.Google Scholar