Systems of conservation laws with third-order Hamiltonian structures
journal contributionposted on 08.02.2018 by Evgeny Ferapontov, Maxim V. Pavlov, R.F. Vitolo
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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