Bi-Hamiltonian structures of WDVV-type

We study a class of nonlinear partial differential equations (PDEs) that admit the same bi-Hamiltonian structure as the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations: a Ferapontov-type first-order Hamiltonian operator and a homogeneous third-order Hamiltonian operator in a canonical Doyle-Potëmin form, which are compatible. Properties of these systems and their classification in low dimension will be discussed.
Joint work with S. Opanasenko.