NEW RESTRICTED FLOWS OF THE KDV HIERARCHY AND THEIR BI-HAMILTONIAN STRUCTURE

We find here new integrable Newton equations which follow from the KdV hierarchy restricted to invariant finite dimensional manifolds called restricted flows. By studying two equivalent algebraic formulations of the restricted KdV vector-field we obtain a bi-Hamiltonian formulation for a natural Hamiltonian system with indefinite kinetic energy. The potential of this Hamiltonian belongs to a larger family of parabolic type potentials which also admit bi-Hamiltonian formulation and which follow from restricted flows of the coupled KdV hierarchies.