Abstract:
We exhibit the bi-Hamiltonian structure of the equations of associativity (Witten-Dijkgraaf-Verlinde-Verlinde-Dubrovin equations) in 2-d topological field theory, which reduce to a single equation of Monge-Ampère type \( f_{ttt}=f_{xxt}^{\;\;\;\;\;2} - f_{xxx}f_{xtt} \, ,\) in the case of three primary fields. The first Hamiltonian structure of this equation is based on its representation as a 3-component system of hydrodynamic type and the second Hamiltonian structure follows from its formulation in terms of a variational principle with a degenerate Lagrangian.
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Received: 1 March 1996 / Accepted: 25 October 1996
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Ferapontov, E., Galvão, C., Mokhov, O. et al. Bi-Hamiltonian Structure in 2-d Field Theory . Comm Math Phys 186, 649–669 (1997). https://doi.org/10.1007/s002200050123
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DOI: https://doi.org/10.1007/s002200050123