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Systems of conservation laws with third-order Hamiltonian structures
journal contributionposted on 2018-02-08, 12:29 authored by Evgeny FerapontovEvgeny Ferapontov, Maxim V. Pavlov, R.F. Vitolo
We investigate n-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classiffication of such systems is reduced to the projective classiffication of linear congruences of lines in Pn+2 satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space W of dimension n + 2, classify n-tuples of skew-symmetric 2-forms Aα ∈ 2 Λ2(W) such that φβγAβ∧Aγ= 0 for some non-degenerate symmetric φ. .
This work was supported by the GNFM of the Istituto Nazionale di Alta Matematica, the Is- tituto Nazionale di Fisica Nucleare by IS-CSN4 Mathematical Methods of Nonlinear Physics, and the Dipartimento di Matematica e Fisica “E. De Giorgi” of the Universit`a del Salento. MVP’s work was partially supported by the grant of the Presidium of RAS ‘Fundamental Problems of Nonlinear Dynamics’.
- Mathematical Sciences
Published inLetters in Mathematical Physics
CitationFERAPONTOV, E.V., PAVLOV, M.V. and VITOLO, R.F., 2018. Systems of conservation laws with third-order Hamiltonian structures. Letters in Mathematical Physics, 108 (6), pp.1525–1550.
- AM (Accepted Manuscript)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesThis is a post-peer-review, pre-copyedit version of an article published in Letters in Mathematical Physics. The final authenticated version is available online at: https://doi.org/10.1007/s11005-018-1054-3