Systems of conservation laws with third-order Hamiltonian structures
FerapontovEvgeny
PavlovMaxim V.
VitoloR.F.
2018
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.
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