A hierarchy of integrable Hamiltonian systems associated with φxx=(λ3−u0−λu1−λ2u2)φ

Abstract

A hierarchy of completely integrable Hamiltonian systems is obtained by restricting a hierarchy of integrable evolution equations associated with φxx=(λ3−u0−λu1−λ2u2)φ to an invariant subspace of the recursion operator of these ev olution equations. The independent integrals of motion in involution and Hamiltonian functions for these systems are constructed by using the recursion formula related to the eigenvalue problem.