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arXiv · 2203.04237

Projective geometry of homogeneous second order Hamiltonian operators

Pierandrea Vergallo·Raffaele Vitolo
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Abstract

We prove the invariance of homogeneous second-order Hamiltonian operators under the action of projective reciprocal transformations. We establish a correspondence between such operators in dimension $n$ and $3$-forms in dimension $n + 1$. In this way we classify second order Hamiltonian operators using the known classification of $3$-forms in dimensions $\leq$ 9. Systems of first-order conservation laws that are Hamiltonian with respect to such operators are also explicitly found. The integrability of the systems is discussed in detail.

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Pierandrea Vergallo, Raffaele Vitolo. 2022-03-08. Projective geometry of homogeneous second order Hamiltonian operators. https://doi.org/10.1088/1361-6544/acf269

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