Bi-Hamiltonian structures of KdV type

  title={Bi-Hamiltonian structures of KdV type},
  author={Paolo Lorenzoni and Andrea Savoldi and Raffaele Vitolo},
  journal={arXiv: Mathematical Physics},
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… 
5 Citations
Computing with Hamiltonian operators
  • R. Vitolo
  • Mathematics
    Comput. Phys. Commun.
  • 2019
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