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Duality for systems of conservation laws

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Abstract

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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Acknowledgements

The author thanks E.V. Ferapontov for useful discussions. This research was supported by FAPESP Grant #2018/20009-6.

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  1. Department of Mathematics, São Paulo State University-UNESP, São José do Rio Preto, Brazil

    Sergey I. Agafonov

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  1. Sergey I. Agafonov
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Correspondence to Sergey I. Agafonov.

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Agafonov, S.I. Duality for systems of conservation laws. Lett Math Phys 110, 1123–1139 (2020). https://doi.org/10.1007/s11005-019-01253-0

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