High Order Ergenvalue Proble And Its Corresponding Bargmann Integrable System Of Eigenvalue Problen

This paper mainly discuss the Bargmann system for the 3th-order complex eigenvalue problem with the energy is depend on speed: Lφ= ((?)3+q(?)2+(?)p+r)φ=λφxFirst introduced some related concepts. After, based on bi-Hamilton operators K, J and Lenard sequence, by the relation between the po-tentials (q,p,r) and the eigenvector φ, the assocoated Lax pairs are nonlinearized, then we found the Bargmann system of the eigen-value problem. According to the Euler-Lagarange equation and the Legendre transforms, contruct a set of Jacobi-Ostrogradsky coordi-nate system has been found. Then the infinite-dimensions Dynamical system can be transformed into the finite-dimendions Hamilton canon-ical system in the symplectic space. So as to obtain the said evolution equations corresponding solutions.