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arXiv · 1508.02752

Towards the classification of homogeneous third-order Hamiltonian operators

E. V. Ferapontov·M. V. Pavlov·R. F. Vitolo
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Abstract

Let $V$ be a vector space of dimension $n+1$. We demonstrate that $n$-component third-order Hamiltonian operators of differential-geometric type are parametrised by the algebraic variety of elements of rank $n$ in $S^2(Λ^2V)$ that lie in the kernel of the natural map $S^2(Λ^2V)\to Λ^4V$. Non-equivalent operators correspond to different orbits of the natural action of $SL(n+1)$. Based on this result, we obtain a classification of such operators for $n\leq 4$.

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E. V. Ferapontov, M. V. Pavlov, R. F. Vitolo. 2015-08-16. Towards the classification of homogeneous third-order Hamiltonian operators. https://doi.org/10.1093/imrn%2Frnv369

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