Seminar talk, 14 December 2016: Difference between revisions
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| title = Bi-Hamiltonian structures of KdV type | | title = Bi-Hamiltonian structures of KdV type | ||
| 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. | | 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. | ||
This is a joint work with Paolo Lorenzoni and Andrea Savoldi. | This is a joint work with Paolo Lorenzoni and Andrea Savoldi. | ||
| video = | | video = | ||
Latest revision as of 23:46, 16 November 2016
Speaker: Raffaele Vitolo
Title: Bi-Hamiltonian structures of KdV type
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.
This is a joint work with Paolo Lorenzoni and Andrea Savoldi.
References:
arXiv:1607.07020