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On the bi-Hamiltonian Geometry of WDVV Equations

Mathematical Physics 2015-07-14 v2 math.MP Exactly Solvable and Integrable Systems

Abstract

We consider the WDVV associativity equations in the four dimensional case. These nonlinear equations of third order can be written as a pair of six component commuting two-dimensional non-diagonalizable hydrodynamic type systems. We prove that these systems possess a compatible pair of local homogeneous Hamiltonian structures of Dubrovin--Novikov type (of first and third order, respectively).

Keywords

Cite

@article{arxiv.1409.7647,
  title  = {On the bi-Hamiltonian Geometry of WDVV Equations},
  author = {M. V. Pavlov and R. F. Vitolo},
  journal= {arXiv preprint arXiv:1409.7647},
  year   = {2015}
}

Comments

21 pages, revised published version; exposition substantially improved