摘要：This paper discusses the second-order matrix eigenvalue problem by means of the nonlinearization of the Lax pairs, then the author gives the Bargmann and Neumann constraints of this problem. The relation between the potentials and the eigenfunction is set up based on these constraints. By means of the nonlinearization of the Lax pairs, the author found these systems of the eigenvalue problem can be equal to the Hamilton canonical system in real symplectic space. In the end, the infinite-dimensions Dynamical systems can be transformed into the finite-dimensions Hamilton canonical systems in the symplectic space. As well, this paper obtains the representations of the solutions for the evolution equations.
