# Bi-Hamiltonian structures of KdV type

@article{Lorenzoni2016BiHamiltonianSO, title={Bi-Hamiltonian structures of KdV type}, author={Paolo Lorenzoni and Andrea Savoldi and Raffaele Vitolo}, journal={arXiv: Mathematical Physics}, year={2016} }

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…

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