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 apparently new integrable systems whose central invariants are non-zero; this shows that new examples are not Miura-trivial.
Lorenzoni, P., Savoldi, A., Vitolo, R. (2018). Bi-Hamiltonian structures of KdV type. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 51(4) [10.1088/1751-8121/aa994d].
Bi-Hamiltonian structures of KdV type
Lorenzoni, P;
2018
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 apparently new integrable systems whose central invariants are non-zero; this shows that new examples are not Miura-trivial.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.