Publicação: Duality for systems of conservation laws
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For one-dimensional systems of conservation laws admitting two additional conservation laws, we assign a ruled hypersurface of codimension two in projective space. We call two such systems dual if the corresponding ruled hypersurfaces are dual. We show that a Hamiltonian system is auto-dual, its ruled hypersurface sits in some quadric, and the generators of this ruled hypersurface form a Legendre submanifold with respect to the contact structure on Fano variety of this quadric. We also give a complete geometric description of 3-component nondiagonalizable systems of Temple class: such systems admit two additional conservation laws, they are dual to systems with constant characteristic speeds, constructed via maximal rank 3-webs of curves in space.
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Congruences of lines, Conservation laws, Ruled hypersurface
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Inglês
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Letters in Mathematical Physics, v. 110, n. 6, p. 1123-1139, 2020.
