Duality for systems of conservation laws

• Autor(a) principal: Agafonov, Sergey I. [UNESP]
• Data de Publicação: 2020
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1007/s11005-019-01253-0; http://hdl.handle.net/11449/198327
• topic: Congruences of lines; Conservation laws; Ruled hypersurface

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.