2134/28436
Evgeny Ferapontov
Maxim V. Pavlov
R.F. Vitolo
Systems of conservation laws with third-order Hamiltonian structures
2018
Loughborough University
System of conservation laws
Linear congruence
Hamiltonian operator
WDVV equation
Projective group
Reciprocal transformation
Quadratic complex
Monge metric
2018-02-08 12:29:32
article
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.
.