CASATI, M. ... et al., 2018. On a class of third-order nonlocal Hamiltonian operators. Journal of Geometry and Physics, 138, pp.285-296.
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.
This paper is in closed access until 9 November 2019.
Matteo Casati was supported by the INdAM-Cofund-2012 Marie Curie fellowship ‘MPoisCoho’. Maxim Pavlov was partially supported by the RFBR grant 17-01-00366. Raffaele Vitolo recognises financial support from the Loughborough University’s Institute
of Advanced Studies, LMS scheme 2 grant, INFN by IS-CSN4 Mathematical Methods of
Nonlinear Physics, GNFM of Istituto Nazionale di Alta Matematica and Dipartimento di Matematica e Fisica “E. De Giorgi” of the Universit`a del Salento