On the integrability of stationary and restricted flows of the KdV hierarchy. (English) Zbl 0870.35092
Summary: A bi-Hamiltonian formulation for stationary flows of the KdV hierarchy is derived in an extended phase space. A map between stationary flows and restricted flows is constructed: in one case it connects an integrable Hénon-Heiles system and the Garnier system. Moreover, a new integrability scheme for Hamiltonian systems is proposed that holds in the standard phase space.
MSC:
35Q53 | KdV equations (Korteweg-de Vries equations) |
37C10 | Dynamics induced by flows and semiflows |