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).
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Pavlov, M.V., Vitolo, R.F. On the Bi-Hamiltonian Geometry of WDVV Equations. Lett Math Phys 105, 1135–1163 (2015). https://doi.org/10.1007/s11005-015-0776-8
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DOI: https://doi.org/10.1007/s11005-015-0776-8