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arXiv · 1607.07020

Bi-Hamiltonian structures of KdV type

P. Lorenzoni·A. Savoldi·R. Vitolo
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Abstract

Combining an old idea of Olver and Rosenau with the classification of second and third order homogeneous Hamiltonian operators we classify compatible trios of two-component homogeneous Hamiltonian operators. The trios yield pairs of compatible bi-Hamiltonian operators whose structure is a direct generalization of the bi-Hamiltonian pair of the KdV equation. The bi-Hamiltonian pairs give rise to multi-parametric families of bi-Hamiltonian systems. We recover known examples and we find new integrable systems whose central invariants are non-zero; this shows that new examples are not Miura-trivial.

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P. Lorenzoni, A. Savoldi, R. Vitolo. 2016-07-24. Bi-Hamiltonian structures of KdV type. https://arxiv.org/abs/1607.07020

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