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On the bi-Hamiltonian Geometry of WDVV Equations

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arxiv 1409.7647 v2 pith:Q53BAMSI submitted 2014-09-26 math-ph math.MPnlin.SI

M.V. Pavlov , R.F. Vitolo This is my paper · ORCID
classification math-phmath.MPnlin.SI
keywords equationsorderpairsystemsthirdtypewdvvassociativity
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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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  1. Compatible pairs of Hamiltonian operators of the first and third orders

    nlin.SI 2026-02 conditional novelty 7.0 of 10

    Compatibility of a first-order weakly nonlocal Hamiltonian operator with a third-order Hamiltonian operator is equivalent to algebraic equations, with the first-order metric fixed by a structure formula in terms of Ha...

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