The Evolution Equation Hierarchy And Its Constraint Flows Related To The Fourth-Order Eigenvalue Problem

In this paper,we discuss the 4th-order eigenvalue problem Lφ = , the Bargmann constraint and perfect C.Neumann constraint of this problem are given,The associated Lax pairs are nonlineared .Then based on the Euler- lagrange function and Leg-endre transforms,a resonable Jacobi-Ostrogradsky coordinate system has been found.The Hamilton cannonical coordinate system equivalent to this egenvalue problem are obtained on the symplectic manifold. It is proved to be a finite-dimensional integrable Hamilton system .Moreover,the constraint flows of the evolution equations in corespondence with this 4th-order eigenvalue problem are generated.