Systems of conservation laws with third-order Hamiltonian structures Evgeny Ferapontov Maxim V. Pavlov R.F. Vitolo 2134/28436 https://repository.lboro.ac.uk/articles/journal_contribution/Systems_of_conservation_laws_with_third-order_Hamiltonian_structures/9385346 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. . 2018-02-08 12:29:32 System of conservation laws Linear congruence Hamiltonian operator WDVV equation Projective group Reciprocal transformation Quadratic complex Monge metric Mathematical Sciences not elsewhere classified