On the integrability of stationary and restricted flows of the KdV hierarchy
On the integrability of stationary and restricted flows of the KdV hierarchy
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 a case it connects an integrable Henon--Heiles system and the Garnier system. Moreover a new integrability scheme for Hamiltonian systems is proposed, …