(1+1)-dimensional integrable Hamiltonian systems reduced from symmetry constraints of the KP hierarchy

A systematic method for getting (1+1)-dimensional integrable Hamiltonian systems reduced from the KP hierarchy is proposed. Namely, the auxiliary linear problems of the KP hierarchy are (1+1)-dimensional integrable Hamiltonian systems by any higher order symmetry constraints. In particular, an infinite common set of integrals of motion are obtained, which are in involution in pairs.