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Classification of pairs of second-order Hamiltonian operators and hydrodynamic type systems in six components

  • Giorgio Gubbiotti
  • Lambertus Van Geemen
  • Pierandrea Vergallo
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Abstract

Following a recent characterisation of hydrodynamic systems with second-order Hamiltonian structure in terms of alternating three-forms on the projective space, we present a complete classification of systems in 6 components. We use non-trivial group action techniques to obtain 5 canonical forms. A general result for every dimension is also obtained for one of these cases, whose geometric structure is strictly related to the symplectic canonical form.

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Cite

BibTeXRIS
BibTeX
@misc{gubbiotti2026classification,
  title = {{Classification of pairs of second-order Hamiltonian operators and hydrodynamic type systems in six components}},
  author = {Giorgio Gubbiotti and Lambertus Van Geemen and Pierandrea Vergallo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19785},
  eprint = {2609.19785},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19785},
}
RIS
TY  - UNPB
TI  - Classification of pairs of second-order Hamiltonian operators and hydrodynamic type systems in six components
AU  - Giorgio Gubbiotti
AU  - Lambertus Van Geemen
AU  - Pierandrea Vergallo
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.19785
UR  - https://arxiv.org/abs/2609.19785
AB  - Following a recent characterisation of hydrodynamic systems with second-order Hamiltonian structure in terms of alternating three-forms on the projective space, we present a complete classification of systems in 6 components. We use non-trivial group action techniques to obtain 5 canonical forms. A general result for every dimension is also obtained for one of these cases, whose geometric structure is strictly related to the symplectic canonical form.
ER  -