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.
Bi-Hamiltonian structures of KdV type
Raffaele Vitolo
2018-01-01
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
