On a class of third-order nonlocal Hamiltonian operators

Casati, M.; Ferapontov, Evgeny; Pavlov, Maxim V.; Vitolo, R.F.

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On a class of third-order nonlocal Hamiltonian operators

journal contribution

posted on 2018-11-06, 13:37 authored by M. Casati, Evgeny FerapontovEvgeny Ferapontov, Maxim V. Pavlov, R.F. Vitolo

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.

Funding

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

History

School

Science

Department

Mathematical Sciences

Published in

Journal of Geometry and Physics

Citation

CASATI, M. ... et al., 2018. On a class of third-order nonlocal Hamiltonian operators. Journal of Geometry and Physics, 138, pp.285-296.

Publisher

Version

AM (Accepted Manuscript)

Publisher statement

This paper was accepted for publication in the journal Journal of Geometry and Physics and the definitive published version is available at https://doi.org/10.1016/j.geomphys.2018.10.018.