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Communications in Mathematical Physics

, Volume 186, Issue 3, pp 649–669 | Cite as

Bi-Hamiltonian Structure in 2-d Field Theory

  • E.V. Ferapontov
  • C. A. P. Galvão
  • O. I. Mokhov
  • Y. Nutku

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.

Keywords

Field Theory Variational Principle Single Equation Hamiltonian Structure Primary Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • E.V. Ferapontov
    • 1
  • C. A. P. Galvão
    • 2
  • O. I. Mokhov
    • 3
  • Y. Nutku
    • 4
  1. 1.Institute for Mathematical Modelling, Academy of Science of Russia, Miusskaya, 4, Moscow 125047, RussiaRU
  2. 2.Universidade de Brasilia, Departamento de Física, 70.910 Brasilia DF, BrasilBR
  3. 3.Department of Geometry and Topology, The Steklov Mathematical Institute, Academy of Science of Russia, ul. Vavilova, 42, Moscow, GSP-1, 117966, RussiaRU
  4. 4.TÜBİTAK - Marmara Research Center, Research Institute for Basic Sciences, Department of Physics, 41470 Gebze, TurkeyTR

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