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arXiv · 1908.00585

Duality for systems of conservation laws

Sergey I. Agafonov
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Abstract

For one-dimensional systems of conservation laws admitting two additional conservation laws we assign a ruled surface of codimension two in projective space. We call two such systems dual if the corresponding ruled surfaces are dual. We show that a Hamiltonian system is autodual, its ruled surface sits in some quadric, and the generators of this ruled surface form a Legendre submanifold for 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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Sergey I. Agafonov. 2019-12-27. Duality for systems of conservation laws. https://doi.org/10.1007/s11005-019-01253-0

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