Letters in Mathematical Physics

, Volume 105, Issue 8, pp 1135–1163 | Cite as

On the Bi-Hamiltonian Geometry of WDVV Equations

  • Maxim V. Pavlov
  • Raffaele F. VitoloEmail author


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).

Mathematics Subject Classification

37K05 37K10 37K20 37K25 


Hamiltonian operator Jacobi identity Monge metric hydrodynamic-type system WDVV equations Casimirs 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Mathematical PhysicsLebedev Physical Institute of Russian Academy of SciencesMoscowRussia
  2. 2.Department of Applied MathematicsNational Research Nuclear University MEPHIMoscowRussia
  3. 3.Department of Mathematics and Physics “E. De Giorgi”University of SalentoLecceItaly

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