2134/35764 M. Casati M. Casati Evgeny Ferapontov Evgeny Ferapontov Maxim V. Pavlov Maxim V. Pavlov R.F. Vitolo R.F. Vitolo On a class of third-order nonlocal Hamiltonian operators Loughborough University 2018 Nonlocal Hamiltonian operator Monge metric Dirac reduction Poisson vertex algebra Mathematical Sciences not elsewhere classified 2018-11-06 13:37:32 Journal contribution https://repository.lboro.ac.uk/articles/journal_contribution/On_a_class_of_third-order_nonlocal_Hamiltonian_operators/9377321 Based on the theory of Poisson vertex algebras we calculate skew-symmetry conditions and Jacobi identities for a class of third-order nonlocal operators of differential-geometric type. Hamiltonian operators within this class are defined by a Monge metric and a skew-symmetric two-form satisfying a number of differential geometric constraints. Complete classification results in the 2-component and 3-component cases are obtained.