%0 DATA
%A Evgeny, Ferapontov
%A Maxim V., Pavlov
%A R.F., Vitolo
%D 2018
%T Systems of conservation laws with third-order Hamiltonian structures
%U https://repository.lboro.ac.uk/articles/journal_contribution/Systems_of_conservation_laws_with_third-order_Hamiltonian_structures/9385346
%2 https://repository.lboro.ac.uk/ndownloader/files/16998542
%K System of conservation laws
%K Linear congruence
%K Hamiltonian operator
%K WDVV equation
%K Projective group
%K Reciprocal transformation
%K Quadratic complex
%K Monge metric
%X 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.
.