Bi-Hamiltonian structures of KdV type
- Resource Type
- Working Paper
- Authors
- Lorenzoni, P.; Savoldi, A.; Vitolo, R.
- Source
- J. Phys. A: Math. Theor. 51 no. 4 (2018), 045202
- Subject
- Mathematical Physics
Nonlinear Sciences - Exactly Solvable and Integrable Systems
37K05, 37K10
- Language
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.
Comment: 21 pages