On a class of third-order nonlocal Hamiltonian operators
journal contributionposted on 06.11.2018, 13:37 by M. Casati, Evgeny 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.
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
- Mathematical Sciences