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EnglishCombining an old idea of Olver and Rosenau with the classifica- tion 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 opera- tors 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 ex- amples and we find apparently new integrable systems whose central invariants are non-zero; this shows that new examples are not Miura- trivial.
| Titolo: | Bi-Hamiltonian structures of KdV type |
| Autori: | VITOLO, Raffaele (Corresponding) |
| Data di pubblicazione: | 2018 |
| Rivista: | |
| Abstract: | Combining an old idea of Olver and Rosenau with the classifica- tion 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 opera- tors 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 ex- amples and we find apparently new integrable systems whose central invariants are non-zero; this shows that new examples are not Miura- trivial. |
| Handle: | http://hdl.handle.net/11587/416408 |
| Appare nelle tipologie: | Articolo pubblicato su Rivista |
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