(untitled) (Journal of Partial Differential Equations, 1997)
Under the constraint between the potentials and eigenfunctions, the Ma eigenvalue problem is nonlinearized as a new completely integrablc Hamiltonian system (R^2N, dp&#8743dq, H): H = 12&#945&#9001&#8743q,p&#9002 - 12&#945_3 &#9001q,q&#9002 + &#9454&#945_3&#951 &#9001q,p&#9002 &#9001p,p&#9002 The involutive solution of the high-order Ma equation is also presented. The new completely integrable Hamiltonian systems are obtained for DLW and Levi eigenvalue problems by reducing the remarkable Ma eigenvalue problem.